MOTION

1.SPEED:

      Example 1. A car travels at uniform speed for  2s and the distance travelled is 50m.

      = It’s speed can be calculated as,

                speed= 50=25m/s

                              2

             S I units : m/s

                

2. A car travels from Kampala to Masaka a distance of about 132km in 3hrs.

        then it’s speed = 132 km/hr.

                                      3

N.B

     The speeds calculated above are average speeds and speed is the distance travelled in a unit time(Rate of change of distance)

           Average speed(u)= total distance travelled(s)

                                           total time taken(t)

                                u = s    while   t = s      ut = s

                                      t                      u

 

DISTANCE-TIME GRAPHS

3. Suppose an object is travelling along a path and we measure it’s distance from one end of the path every second, the results are shown in a table below:

     Time(s)       0     1     2     3     4     5     6     7       8     9      10

   Distance(sm) 0    15   30   45   60   75   90   105  120  135   150

 

Draw a distance-time graph for the motion above :       

Diag.1

 


                   45                

 

                   30                           

 


                   15

 

 


                                     1        2             3

 

Because of the straight line graph obtained, the speed was constant or uniform (the object covered equal distances in equal intervals of time).

Uniform because 1-2nd, s = 15m/s

                                          

 

 

 

 

Non-uniform speed graph

 


distance(m)

 


  45                                                                     D

 

 

 

  15                  B                       C

 

 

 

 

      

     A                                                                               time(s)

                        1                         2                      3

 

 

 

4. Consider an object travelling and its distance covered is recorded every after every second:

                     time(s)   0    1     2     3     4     5       6      7     8     9     10

  distance travelled(m)  0   20   40   60   80  100  100  100  100  105  110

 

Plot a graph of distance against time and;

*calculate speeds for each portion of graph

* calculate average speed = 110 =11m/s

                                              10

N.B: the object never travelled at 11m/s anywhere. The uniform speeds where 20m/s, 0m/s and 5m/s.(but an object starting from the same place moving at 11m/s would cover the same distance in 10s)

 

EXERCISE 1: The motion of an object is recorded in the table shown below:

            Time(t)(s)           0     1     2     3     4     5     6     7     8     9     10

  Distance travelled(m)   0    5    10   15   20   30   40   50   50   52    54

 

(i)                  plot a distance-time graph

(n)              describe the motion of the object, giving it’s speed at different stages of it’s journey. What is the average speed for;

a)      the first 5 seconds of the journey?

b)      The whole journey?

 

 

 

 

 

SPEED-TIME GRAPHS 

 

From example (3) and (4), speed-time graphs can be obtained.

 

e.g (3)

 


                                                                                     distance travelled = area under            

           speed(m/s)                                                                                            graph

 

                                                                                                             = 15 x 10 = 150m                

 

 

 

                                                                             10s

                                                                      Time(s)

 

 e.g.(4)                    

                 speed(m/s)

 

 

                          20(m/s)

 

 

                            5m/s

 

 

                                          

                                       1               5                      8                10  time(s)

 

 

 

EXERCISE 2: Plot a speed-tiem graph for the object of the table in exercise 1. Calculate the areas under the curve and find the total distance travelled.

 

SCALAR AND VECTOR QUANTITIES

 

Example 1: If a girl moves in a straight line at a uniform speed of  2m/s and it takes her 4s to move from point  X to Y and back again to X,

 

   X                                                                                       Y

  

Plot a distance-time graph for the girl.

   T(s)   0   1   2   3   4   5     6    7    8     

 S(m)   0   2   4   6   8   10   12  14  16

 

 

                  S(m)

                    16m

 

                                                                                        gradient = +2

                                                                                           speed = 2m/s

                

             

                   

               

                          0     1                              8      t(s)

 

ii) plot a displacement time graph,

                                t(s)     0    1    2    3    4    5    6    7    8

displacement(s) from X    0    2    4    6    8    6    4    2    0

 

                    s(m)                                                           gradient I = +2

                                                                                      gradient II = -2

                       8                                   

                                                                                           velocity I = +2m/s

                                 I               II                                          velocity II = 2m/s

 

   

                         0            

4                      8 t(s)

              

VELOCITY:

 Considering the displacement-time graph, the gradient of  the graph gives

                                          g = displacement

                                                       time

This is also called the rate of change of displacement. This quantity is also called Velocity(units m/s).

Using graph (i), from point X toY the velocity was +2m/s in the first 4s and a velocity of –2m/s from Y to X in the next 4 seconds. Therefore velocity is speed in a particular direction.

N.B: A car turning a corner or moving in a circle at 10m/s has a steady speed but it’s velocity is always changing because it’s direction also changing continously.

                                                               10m/s

                                                                C

 

                                               

                                 10m/s      D                        B      10m/s

 

 

     

                                                              A            10m/s

 

Example 2: A ball thrown vertically into the air with a velocity of  50m/s. It rises for 5sec., stops and then falls downwards to reach 50m/s in a further 5seconds.

i) plot a graph of speed against time for the balls motion.

 

Speed 50m/s

 

 

 

                               I                          II                            gradient I = -10m/s

 

                                                                                         Gradient II = 10m/s

                                                                                          Distance 125 x 2 = 250m

                                                                                            (area under graph)

 

                     0                    5                      10             t(s)                           

 

The speed is decreasing at a rate of –10m/s and then increasing at the same rate.

 

ii) Plot a velocity-time graph for this motion.

                                                                                                                                    

            velocity(m/s)

                        

                            50

 

 

 

                                                   5s                                          time(s)

 

 

 

 

 

                             50

 

 

           displacement =(1x5x50) + (1x5x-50) = 0       

2                                  2

              the ball returns to it’s original position.

 

 

ACCELERATION

 

EXERCISE 1: An automobile starts from rest and it’s motion is described in the table below;

Time(s)             0     1       2       3      4       5       6       7       8       9       10

Velocity,u,(m)  0     5      10     15     20    20      20    17.5   15    12.5   10

i)                    plot a velocity-time graph to show how its velocity changes during its journey.

ii)                   Calculate the area under the graph (total displacement)

 


Velocity(m/s)

                                                         B               C                                         

                                                                                       

                                                                                        17.5

 

                                                       60       80

                                           

                                                                                                                         D

                                      22.5  40

 

                                 10  

                      A  

                                                     4        5          6          7          8        9         10  time(s)

iii)                 Analyse the motion;

       -During the 1st 4s, the velocity of the body increases at a rate of 5m/s every second(we call this uniform acceleration)

        therefore acceleration =gradient = velocity change

                                                                 time taken      

(definition- rate of change of velocity)

    -During the next 2s, velocity is constant and zero rate of change of velocity,

              therefore zero acceleration.                              

 In the last 4 seconds, gradient is –ve;   grad. = -2.5m/s

                                                                 Acc.= -2.5m/s

    Therefore velocity decreases at a rate of 2.5m/s every second. This negative acceleraton is often called deceleration or RETARDATION.(when acceleration’s direction opposes velocity direction).

            iv)i) Make a table to show the displacement during each second of the journey

          ii) Find the total displacement in the motion above

               iii) Draw a displacement-time graph for the data obtained in (ii) above

             

            QUESTIONS

 

 1. An antelope starts from rest and accelerates uniformly in a straight line. It reaches a velocity of 20m/s after it has travelled 180m. Find its acceleration and the time it takes to cover this distance.

 

2. A train travelling at 60m/s decelerates to 40m/s. During the period of deceleration, its displacement is 2km. How long does deceleration take and what is the rate of deceleration?

 

3. An automobile passes the speed limit sign at the edge of a town when it’s travelling at 10m/s. It accelerates at 1m/s for 15s. Then it travels at uniform velocity for 3minutes. Next the driver driver sees a level-crossing gate 500m ahead. He decelerates uniformly bringing the automobile to rest at the gate;

 i) What is the highest velocity reached by the automobile?

ii) What is the time spent decelerating?

iii)What is the the displacement(distance) between the speed limit and the level gate?

iv) What is the total time of the journey?

v) What is the average velocity for the whole journey?

 

4. A butterfly flies beside a fence, the posts of which are 1m apart. The time at which it passes each post is recorded in the following table;

   Post number(displacement,s, in meters)        0      1       2        3        4        5

                                    Time, t, in seconds        0      2      4.5    6.25    8.35   10.4

i) Plot a displacement –time graph.

iv)                 Is the butterfly’s velocity uniform?

v)                  During which part of the journey is its velocity greatest?

vi)                 What is its greatest velocity?

vii)               Is the acceleration uniform over the whole journey?

 

EQUATIONS OF MOTION

 

Consider a velocity-time graph shown below. The body with velocity(u) when timing starts. It has a uniform acceleration of A m/s which means that each second its velocity increases by A and after T(seconds), its velocity will have increased by AT. If  the final velocity is V,

                       Vm/s

 

                              V                                                 A

                                     Gradient = a

                                                                II

                           U                                                   

                              C                                                  B

 

                                                         I

 

 

                               

                                0                                              t                  time(s)

                                       gradient = AB   = AB =  a    } = AB = at

                                                        CB         t                               

                                       Therefore V= u + at (i)(velocity-time equation)

                                     If the object starts from rest, then u = 0 and v = at

The displacement of the object is represented by the area under the curve

i.e            area of the rectangle + area of triangle

            =                  ut               +    1 x t x  at

                                                         2

                  s =           ut               +   1at2

                                                         2

                   therefore s = ut + 1at2- (2)(displacement-time equation)

 

Method II

                  Area under curve = Area of trapezium

 

                                                                Area = 1(u + v) t

                                                                                2

                                                              s = (u +v)t   (3)(displacement time equation

                            u                          v              2

                                                               average velocity x time

                                                                but also from(1)  v = u+at

                                         t                                             =     v - u = t

                                                                                                 a

                                                               in (3) s = (u+v) (v – u)

2                  a

                                                                   

 

 

 

 

 

 

N.B: These equations apply to only situations with uniform acceleration.

 

EXAMPLE 1: A cyclist starting from rest with uniform acceleration can reach a velocity of 20m/s in 25seconds. Calculate her acceleration.

 

2. I f a car can accelerate uniformly at 2.5m/s and starts from a velocity of 36km/h, find its velocity after 8 seconds.

 

3. a car accelerates uniformly from rest for 20s with an acceleration of 1.5m/s. It then travels at a constant speed for 2minures before slowing down with a uniform deceleration to come to rest in a further 10s. Sketch a velocity-time graph of the motion and find;

a)      the maximum speed

b) the total distance travelled and

c) the acceleration while slowing down.

 

4. If a train accelerates uniformly from rest at 0.2m/s over a distance of 1km, calculate the velocity it reaches.

 

PROJECTILES

Falling objects such as a ball, discuss or stone that is thrown away, a bullet fired from a gun, and water from a fireman’s horse pipe are all examples of projectiles.

A projectile at once starts to fall under the action of gravity below the  direction in which it was fired or thrown. It continues to fall all the time it is moving and its downward acceleration is constant(neglecting air resistance).The part of a projectile is (almost) the arc of a parabola commonly called a trajectory

 

Example (1) a coin on the edge of a bench given a sharp blow;

 

 

 


                              

                                bench                                  path of falling coin

 

 

 

 

                                                                                          floor

                                                                                          

 

   (2) A ball projected above the ground

 

 

 

 


                                                                                                            path of the ball

                                                                                                            (trajectory)

 

 

                                                                                                                

 

As the ball moves along its path, it gets displaced horinzotally and vertically if the ball is kicked off with velocity (u) inclined at an angle q to the ground.

                                                        

                                                                                                                     

                                             

                                        u         

                                                            u sin q

                               q

                                      

                                   u cos q

The ball has an initial velocity 0f u cos q horizontally and u sin q vertically and it moves freely under gravity with acceleration = 0 in the horizontal plane and acceleration = -g in the vertical plane.

 

Example 1: A bullet fired horizontally from a gun has an initial velocity of 50m/s. The bullet falls to the ground after 4s. Calculate;

a)      the vertical distance of fall of the bullet and

b)      the horizontal distance travelled by the bullet.

 

                        50m/s                       initial horizontal velocity = 50m/s

                                                                                       t = 4s

                                                                   initial vertical velocity = 0m/s

                                                                                                     t = 4s

h                                                                                         a = +gm/s2

                                                                         s = ut + 1 at2

                                                                                        2

                                                                              = 0 x 4 x1x 9.8x16

                                        x                                                  2

                                                                                   = 4.9x16

                                                                                     = 78.4m

                                                                  horizontal distance = v x t

                                                                                                = 50 x 4

                                                                                                = 200m

 

MOTION UNDER GRAVITY

1.      An object falls from the top of a cliif 122.5m high. Find the time taken to reach the sea and the velocity of the stone when it does so.

2.      A stone thrown downwardsfrom a cliff with a velocity of 4m/s reaches the sea in 3s. Find the height of the cliff.

3.      A rocket is projected vertically upwards with a velocity of 490m/s. Find the

a)      height reached

b)      time taken to return to the ground

c)      velocity with which it hits the ground.

4.      An object released from a helicopter rising at 12m/s reaches the ground in 10s. What is the height of the helicopter at the time of release?

              a = 9.8m/s2

                     t = 10                                       u =12m/s

              u = 12                                      a = -9.8m/s

              s = ut + 1at2                                          120 + 490 =

                                        2

             = -12.10 + 1.9.8.102                            t = 10s

                             2

                =  -120 + 490                          s = ut + 1at2

                                                                           2

                     = +370m                           12 x 10 – 1.9.8.100

                                                                               2

                                                                      = -370m

5.      A ball is thrown vertically upwards at 20m/s. Calculate ;

a)      how high it rises

b)      the time taken to reach this maximum height

6.      If a stone is dropped from rest down a well and a splash is heard after 2.5seconds, how deep is the well?

7.      A ball is thrown vertically upwards and reaches a height of 28.8m. Ignoring the effects of air resistance and taking g = 10m/s, find;

a)      the initial upward velocity and

b)      the time taken to return to the handa of  the thrower

 

INERTIA AND MASS

The property of a body to remain at rest or if moving, to keep on moving in a tsraight line is called Inertia.

Examples:

i)                    Aperson standing in a bus which starts to move forward suddenly tends to fall backwards(the reason is that her feet move with the bus but the body tends to remain at rest) whereas the person falls forward if the bus stops. The feet stop but her body tends to keep moving.

ii)                   Also when the bus turns a sharp corner, the person tends to move in a straight line.

Definitions: Mass is the quantity of matter in a body. The mass ofa body measures its inertia. A large mass is more difficult to move from rest than a small mass and it is more difficult to stop when it is in motion. Therefore the bigger the mass, the bigger the inertia.

To demonstrate Inertia;

1.      Place a book on a smooth cloth on a table. Pull the cloth away with a quick jerk.The book remains at rest on the table.

2.      Place a coin on a small card on the edge of a table so that it sides stick out. Hit the card firmly with one finger. The card moves but the coin remains where it is.

3.      Make a pile of ten cent coins. Knock the bottom coin from the pile by hitting it sharply with a thin ruler. The coin that is hit moves but the other coins stay in position.

4.      Suspend two identical tins by separate long strings of equal length. Fill one of the tins with sand or similar heavy material. Now give the same push with a finger or hand separately to the tins; which tin swings more? Let the tins come to rest and then pull them to equal distances to one side and release them, try to stop each tin with the same force from your finger or hand; which tin is easier to stop and  why? ( the sizes of the tins are the same but their inertias are different. The tin with sand has greater inertia and is more difficult to move and when moving, more difficult to stop). If theses experiments on the moon or in outer space, the results would be the same. A body is just as difficult to start, stop or accelerate no matter where it is because its inertial mass is constant and is the same everywhere in the universe.

 

NEWTON’S LAW OF MOTION

1.      FIRST  LAW:( sometimes called the law of inertia)

            A body at rest will remain in its state of rest or a moving body continue in uniform motion in a straight line unless it is acted upon by an external force to act otherwise( i.e the velocity of a body will not change unless a force acts on it)

 

2.      SECOND  LAW: ( Momentum)

              This is the product of the mass and velocity of the body.

                 i.e  momentum = mass(kg) x velocity(m/s)

                 S I unit for momentum = kgm/s

Newton’s 2nd law states that when two or more bodies act upon one another, their total momentum remains constant provided no external forces are acting.

 

       Examples:

1.      Find the momentum of;

a)      a car of mass 1000kg moving at 20m/s

b)      an oil tanker of mass 100 x 106kg moving at 5m/s

c)      an electron of mass 9 x 10-31kg moving at 2 x107m/s

Newton’s second law states that “ the rate of change of momentum of a body is proportional to the applied force and it takes place in the direction in which the force acts.

     Consider a body of mass M and having a velocity of Um/s. If it accelerates toa velocity of Vm/s in time T, then

                                                    v- u = a         f * a

                                                      t               therefore f = ma = f =m( v – u)

                                                                                                                  t

and change in momentum is ( mv – mu)

                                                      t

     rate of change of momentum     F *  mv –mu

                                                                     t

                                                         F * m(v – u)

                                                                       t

                                                         F * ma       <=> Force = constant x ma

Note: F = ma

         F(N) = m(kg)  a(ms-2)

          1N = 1kg x 1ms-2

Therefore a newton is a force required to give a force of 1kg an acceleration of  1ms-2.

 

Examples: 1. Find the acceleration of a body of mass 10kg when it is subjected to a ho     horizontal force of 100N if it ;

a)      can move along a smooth horizontal surface.

b)      Can move along a horizontal surface which produces a frictional force of  80N

 

2.Aracket of mass 800,000kg has motors giving a thrust of 9,800,000N, find the acceleration at lift off.

3. A force of 100N acts on a mass of 1kg. What is the acceleration?

4. A force of 5Nacts on a stationery mass of 2kg which can move along a smooth horizontal surface. What is its velocity after 5s?

 

3.  THIRD  LAW :

            It states that to every action there is an equal and opposite reaction i.e if a body A exerts a force on body B, then body B exerts an equal but opposite force to A.

e.g a book placed on a table;

 

                                                    R

                                               

                                              W

Example to illustrate action and reaction:

 

a)      Walking and running; you exert a force/ action with your feet on the ground and the ground exerts a reaction on your feet. The reaction is caused by friction between your feet and the ground. If it’s a smooth ground, you can slip and fall because of the small friction. A sprinter uses starting blocks to give her sufficient reaction when starting.

 

b)      Rowing a boat; the oars exert a force on the water and the water exerts an equal and opposite reaction on the oars. So the boat moves forward while the oars and the water are pushed backwards.

 

c)      Recoil of a rifle; when you fire a rifle, the action accelerates the bullet forwards while the reaction accelerates the rifle backwards.

 

d)      Rockets; blow up a baloon and then release it. The escaping air exerts an action downwards and equal and opposite reaction moves the baloon upwards.

In a rocket the hot exhaust gases produced by combustion of the fuel liquids or solids exert an action downwards and the rocket moves and accelerates upwards.

 

Examples:

1.      A cage of mass 100kg is held by a cable. Find the tension in the cable when;

a)      held at rest

b)      lowered with constant speed of 1m/s

c)      raised with constant acceleration of 1m/s

 

LAW OF CONSERVATION OF MOMENTUM

 

When two or bodies act upon one another, their total momentum remains constant provided no external forces are acting.

 

Example 1.

       A projectile of mass 200g moving at 800m/s hits a movable target of mass 10kg which is at rest. The target and projectile move on together after the impact. Find;

a)      the momentum of the projectile

b)      the combined velocity just after the impact

 

a)         momentum = m x v

                          = 0.200 x 800

                          = 160Ns

b)        By principle of conservation of momentum,

                     momentum before impact = momentum after impact

                      (0.200 x 800) + (10kg x 0) x v

                                  160    =   10.2v

                                        

                                     v = 160

10.2          =  15.7m/s

2.      A bullet of mass 50g moving at 100m/s becomes embedded in a stationary suspended target of mass 5.0kg. What is their combined velocity just after impact?

                  Momentum before = momentum after

                     50 x 100 + 0        =   (50  + 5)v

                    1000                          100

5= 5.05v

v = 5        =  0.99m/s   

     5.5

3.      A railway truck of mass 1800kg moving at 4.0m/s collides with a truck of mass 1200kg moving in the same direction at 3.0m/s. If they move on together, what is their combined velocity after collision?

              

         Momentum before  =  momentum after

       (1800 x 4) + (1200 x 3)  = (1800 +1200)v

          7200       +   3600       =     3000v

             10800   =    3000v

3000                    3000

         v = 3.6m/s

 

4.      A 20kg projectile leaves a 1200kg launcher with a velocity of 600m/s forward. What is the recoil velocity of the launcher?

           

       Momentum before      =    momentum after firing

       (20 x 0) + (1200 x 0)  =   1200(-v) + (20 x 600)

0        =  12000 – 1200v

v    =  12000    = 10m/s

                                    1200

5.      A large space rocket has motors which eject 11,000kg of propellant per second with a velocity of 3000m/s. What thrust does this produce?

  

Momentum of propellant released per second = 11000 x 3000 = 33 x 106Ns.

Reaction force onto the rocket = 33 x 106Ns = F,

                            F = 3.3 x 106N

 

TURNING EFFECTS OF FORCES

 

   The moment of a force about a point is the product of the force and the perpendicular distance of its line of action from the point.

   Moment is the measure of the turning effect of a force. The moment of a force depends on; i) the magnitude of a force

                  ii) the perpendicular distance of line of action of force from the point of reference.

 

Experiments to study moments:

A meter rule is balanced on a fulcrum(a knife edge) and weights w1 and w2 land on either sides.

 

       A                                                                      B

 

                        X                                     Y

       w1                           fulcrum(pivot)                w2

       

When the metre rule balances horizontally to a good approximation,

               w1x = w2y

 

The principle of moments:

             For a body in equilibrium, the sum of the anticlockwise moments about any point is equal to the sum of the clockwise moments.

Parallel Forces

     Parallel forces acting in the same direction are called like forces and those in opposite directions are unlike forces.

     A pair of unlike forces are called a couple of forces.( a couple of forces is a pair of equal and opposite forces acting on a body and their lines of action are parallel).

 

                                F

 

 

 

 

 

 

F

 

Centre of gravity:

       A body is made up of tiny particles each experiencing the earth’s pull. The earth’s pull on the body thus consists of many equal parallel forces;

 

                                                        

                                                                  

                                                      

                                                          

                                                               

                                            G                             

                                     w         w

                    w   w                             w

 

                                             w

 

At every point there is a weight w, so this gives a resultant earth’s pull which is equal to the total weight w of the body which acts through a point G in the body. The centre of gravity G is the point of application of the resultant force on the body due to the earth’ 

REVISION  QUESTIONS

 

1.a) A ticker-timer vibrates at a frequency of 50Hz. The distance between 2 dots is 4cm. Find;

 i) the time that elapses between two consecutive dots.

ii) the average speed of the tape.

b) The ticker-timer if (a) above was used to measure acceleration of a body which gave the following information.

Distance between 4th and 6th dot = 3cm

Distance between 6th and 8th dot = 7cm

What value was obtained for the acceleration?

 

2.A man who can swim at 3m/s in still water crosses a river which is flowing at 4m/s. He swims perpendicularly to the flow of the river.

a) Sketch a diagram to show his resultant velocity.

b) If the river is 300m wide, how long will he take to cross it?

             

3.          .  A    .      .    .       .       .      .B   .      .       .    

 

                   2cm                                       5cm

 

The tape above was produced by a ticker-timer vibrating at a frequency of 10Hz. The tape was being pulled by a trolley rolling down a slope.

  i) calculate the velocity in region A.

 ii) calculate the velocity in region B.

iii) find the change in velocity from region A to region B.

 iv) calculate the time taken to move from region A to B.

  v) calculate the acceleration of the trolley.

 

4. Use the questions  above in all the cases below.

 

 


a)              A                                         B

           .   .   .   .   .   .       .      .        .        .        .      .

              

              1.5cm                                 8cm

 

The above tape was produced by a ticker-timer vibrating at a frequency of 50Hz.

 

 


b)                      A                                            B

             .             .         .          .     .     .     .     .     .

                       6cm

                                                                     2cm

 

 

The above tape was produced by a ticker-timer vibrating at a frequency of 20Hz.

 

c)                        A                                                   B

                      .    .    .    .    .      .     .      .      .     .       .       .    .    .    .

 


                                     3cm                                          6.5cm

 

The above tape was produced by a ticker-timer vibrating at a frequency of 50Hz.

 

5. The diagram shows two sections of one tape obtained from a ticker-timer experiment.

              10       11         12            35             36             37

            P.          .           .Q             R.               .                .S

 


                     2cm                                     5cm

 

i) calculate the average velocity of the trolley between dots P and Q and R and S.

ii) calculate the acceleration of the trolley.

iii) what force was applied to this trolley of mass 100g to give this much acceleration.

 

6.A stone is thrown with a horizontal velocity of 50ms-1 from the top of a cliff. It takes 4seconds to land. Find;

 i) the height of the cliff.

ii) the horizontal distance travelled on landing.

iii) the vertical velocity attained on landing.

 iv) the horizontal velocity on landing.

 

7. A boy playing football on a shade at the top of a building kicks the ball and it leaves the shade with a horizontal speed of 30ms-1. If it falls through a horizontal distance of 150m on landing, find;

 i) the time the ball takes to land.

 ii) the height of the building.

iii) the vertical velocity of the ball on landing.

 

8. Calculate the velocity of a ball after 4s if it is initially travelling vertically downwards at 5ms-1.

 

9. A boulder is sliding down a slope with a uniform acceleration of 3ms-2. If its starting velocity was 2ms-1, calculate its velocity after it has slid 10m down the slope.

 

10. A motor car is uniformly decelerated from 90kmh-1 to 18kmh-1 in a time of 10s. Calculate the acceleration.

 

11. A rocket is uniformly accelerated from rest to a speed of 960ms-1 in 1 2/3 minutes. Calculate the distance travelled.

 

 

12.a) State Newton’s laws of motion.

b) A block of wood of mass 245g is sent sliding along a rough horizontal table, the initial speed being 3m/s. If the resistance to motion is 0.5N, find the distance travelled and the time taken before the block comes to rest.

 

13. A projectile of mass 200g moving at 400m/s hits a movable target of mass 10kg which is at rest. The target and projectile move on together after the impact. Find;

 i) the initial momentum of the projectile.

ii) the combined velocity just after the impact.

 

14. A bullet of mass 100g moving at 100m/s becomes embedded in a stationary suspended target of mass 10kg. What is their combined velocity just after impact?

 

15. A truck of mass 900kg moving at 8m/s collides with a truck of mass 1000kg moving in the same direction at 5m/s. If they move on together, what is their combined velocity just after the collision?

 

16. A 10kg projectile leaves a 1200kg launcher with a velocity of 500m/s forward. What is the recoil velocity of the launcher?

17. A large space rocket has motors which eject 11,000kg of propellant per second with a velocity of 3000m/s. What thrust does this produce?

 

18. A man of mass 100kg stands on a weighing machine in a lift. The lift moves upward with an acceleration of 0.6m/s2 for a short time and after moving with constant velocity for a brief period, is brought to rest with a retardation of 1.0m/s. Find the reading of the weighing machine during the three phases of the motion.

(i.e upward acceleration, constant velocity, retardation).

 

Projectiles:

19. A stone is thrown horizontally from the edge of a cliff 40m above the sea. Given that the stone travels 60m horizontally before it hits the water, find;

 i) the time for which it is in the air and its initial speed.

ii) the velocity of the stone as it hits the water.

 

20. Find the acceleration of the trolley tape below if the timer is vibrating at 50Hz.

 


                         .        .       .

 

 


                       2.6cm   3.4cm

21. The piece of tape below was made with a ticker-timer vibrating at 40Hz. What was the acceleration of the trolley?

                                     .       .          .         .

 


                                                2.5cm     1.2cm

22. If the trolley is vibrating at 10Hz, find the acceleration of the trolley from the tape below.

                      .       .      .       .       .       .       .        .   

                           

                                 3cm                                  1.5cm           

 

 


23.             .     .     .     .     .    .     .     .     .     .     .     .     .     .

 


                          X1 cm                                               X2cm

 

 

If the tape above is from a timer vibrating at 50Hz., find the acceleration of the trolley.

 

24. A ticker-timer vibrates at a frequency of 10Hz. The distance between two consecutive dots is 3cm and the distance between the 4th and 5th dots is 4cm, calculate the acceleration of the tape.

 

25. The diagram below shows dots produced on a tape pulled through a ticker-timer by a moving body. The frequency of the ticker-timer is 50Hz.

                                                         Tape

 


 Direction of         .           .                   .                         .                         .  

Motion           

 


                                 2cm                                                          5cm

Calculate the acceleration of the body.

 

26. A car starting from rest accelerates at a rate of 2ms-2 for 20seconds,it moves at constant velocity for 20seconds before uniformly brought to rest in 8 seconds.

Draw a sketch graph of velocity against time for the motion.

 

27.a) What is the difference between speed and velocity?

b) The graph shows the variation of distance with time for a body. Describe the motion of the body.

                        300

 distance(m)    200

                        100

                              0

                                    8       16   24      32  time(s)

c) Describe an experiment to demonstrate friction compensation using an inclined plane.

 

d) The figure below shows dots produced on a tape pulled through a ticker-timer by a moving body.

 

 

Direction of

motion

                               2cm                                           5cm

                              

28.a) Distinguish between speed and velocity.

b) A ball is thrown vertically upwards. Sketch graphs which represent;

 i) the variation of velocity of the ball with time.

ii) the distance travelled by the ball against time.

c) A stone was projected horizontally at 20ms-1 from the top of a building 30m high;

 i) Name the path traced by the stone.

ii) What horizontal distance is covered by the stone from the bottom of the building?

d) i) State the principle of conservation of momentum.

 ii) What is meant by an elastic collision?

iii) A 2kg steel ball moving at 4ms-1 collides head-on with another of mass 1.5kg moving at 3ms-1 both on a horizontal smooth surface. If an inelastic collision occurred, determine their velocity after collision.

 

29.a) What is meant by the following terms;

i) Velocity       ii)Acceleration

b) An object of mass 2kg is moving with a velocity of 1ms-1. It is then acted upon by a force of 5N through a distance of 16m. Calculate;

  i) the acceleration produced by the force.

 ii) the final velocity of the object.

iii) the work done by the force.

c) State the principle of conservation of momentum.

d) A trolley of mass 3kg moving at 8m/s collides head on with another trolley of mass 2kg moving at 4m/s in the opposite direction. The trolleys move together after collision.

 i) What type of collision is this?

ii) Determine the common velocity after collision.

 

30.a) Define acceleration.

b) A body of mass 4kg is pulled along a smooth horizontal bench by a string which passes over a pulley and carries a 2kg mass on its other end.

                                            T

                      4Kg

                                                            T

                                                          

                                                        2kg

Find the acceleration of the system and the tension in the string.

 

31.a) What do you understand by the term “uniformly accelerated body”?

b) A body moves with constant acceleration for 5s starting with a velocity of 3ms-1. It then moves with uniform velocity for 8s after which it is non-uniformly restarted for further 2s to come to rest.

 i) Sketch a velocity/time graph for the motion.

ii) Find the distance covered by the first 5 seconds.

 

32.a) What is meant by kinetic energy and potential energy?

b)

                                                ball

 

 

 


             1m                                spring

 

 

                                                table

                           fig.2

 

A ball of mass 100g falls from rest through a height of 2m onto the top of a spring of length 1m, placed on a table as shown in figure 2 above.

 i) How much energy is passed on to the spring by the ball?

ii) If the elastic constant of the spring is 100Nm-1, what will be the compression in the spring?

 

33.a) A car is uniformly accelerated from a velocity of 8ms-1 at a rate of 3m/s-2 for 5s. The brakes are then suddenly applied and the car comes to rest in a further 7s.

  i) Sketch a velocity-time graph for the motion.

 ii) Calculate the maximum velocity attained.

iii) Find the total distance covered.

 iv) What could be the possible reason for this sudden braking?

  v) What caused the car to stop?

b) A girl throws a stone horizontally from the edge of a cliff into a lake to hit a fish at a velocity of 25ms-1. It strikes the water surface at a distance of 80m from the base of the cliff. Determine the height of the cliff.

c) Food parcels to be dropped from an aero plane flying horizontally, have to be released a little before the plane is vertically above a relief camp. Explain this observation.

 

34.a) Define the following terms;

  i) Velocity

 ii) Acceleration

iii) Momentum

 iv) Displacement

b) Sketch displacement-time graphs for a body;

  i) with uniform velocity.

 ii) uniform acceleration

iii) at rest.

 iv) increasing acceleration.

c) A car starts from rest and is accelerated uniformly at 2.4m/s2 for 25 seconds. It moves with the velocity thus attained for 5 minutes and then accelerated again  at 1.3m/s2 for 6 seconds. It is then brought to rest with uniform retardation in another 8 seconds.

 i) sketch a velocity-time graph for the motion of the car.

ii) calculate the maximum velocity attained, the total distance moved and the average velocity.

 

35.ai) Define the terms velocity and reaction time.

ii) A steel ball-bearing is released from rest and let to fall through a tall jar with filled with oil. Sketch a velocity-time graph for the motion.

b) A car travelling at a velocity of 10m/s is uniformly accelerated at a rate of 3m/s2 for 5s. It then moves at the maximum speed attained for 8s. The driver then sees a school girl crossing the road. He applies the brakes bringing the car to rest in 2s.

 i) Sketch the velocity-time graph.

ii) calculate the total distance covered.

c) An object of mass 4kg is dropped from a height of 100m from a helicopter. The air resistance acting against the paracute exerts a steady upwards force of 35N. Calculate the kinetic energy of the object when it reaches the ground.

 

36.a) State Newton’s law of motion.

b) A minibus of mass 576kg can accelerate from rest to 72Kmh-1 in 20s. If the acceleration is assumed uniform, find this acceleration and the attractive force in Newtons needed to produce it.

c) A mass of 2kg projected along a flat surface with a velocity of 15ms-1 comes to rest after travelling 30m. What is the frictional force?

 

37.a) State the law of conservation of momentum.

b)         

                     A         10m/s         B

                                

 

In the figure above, spheres A and B are resting on a smooth surface. A has a mass of 2Kg and is projected towards B of mass 3Kg with a velocity of 10m/s. It collides and gets stuck to B so that they move together. Find the common velocity.

 

38. A falling body pulls a length of paper tape through a stationary vibrator which prints 50 dots on the tape each second.

a) What time does it take the vibrator to print 10 dots?

b) If the distance from  the 10th to the 20th dot is 30cm and that from the 20th to the 30th is 50cm, calculate the acceleration of the tape.

 

39. An object of mass 2Kg is moving with a velocity of 1ms-1. It is then acted upon by a force of 5N through a distance of 16m.

Calculate:-

a) the acceleration produced by the force.

b) the final velocity of the object.

c) the work done by the force.

 

40.a) Define acceleration.

b) A car of mass 1000Kg was moving at 80Kmh-1 when its engine is switched off. If a constant frictional force of 2500N acts on the car, how long will it be before the car stops from the time the engine is switched off?

 

41.a) Define the following:-

 i) Displacement    ii)Momentum

b) Sketch graphs of velocity-time for a body moving with;

 i) zero acceleration

ii) acceleration which increases with time.

c) A body of mass 4kg is moving initially at 10m/s. An accelerating force is applied to the body such that after a time of 4seconds, its velocity is 30m/s. Sketch the velocity-time graph and calculate:-

  i) the change in velocity of the body.

 ii) the distance travelled during the 4seconds.

iii) the acceleration of the body.

 iv) the work done by the accelerating force.

 

42.a) What is momentum?

b) State the law of conservation of momentum.

c) A bullet of mass 20g is fired with a speed of 250m/s from a rifle of mass 2.0kg. What is the initial recoil speed in m/s of the rifle?

 

43.a) Define the following terms as applied to motion:-

  i) displacement

 ii) velocity

iii) momentum

b) A body of mass 4kg is moving initially at 10m/s. An accelerating force is applied to the body such that after 4sec. Its velocity is 30m/s.

  i) Sketch the velocity-time graph for this motion.

Calculate:-

 ii) the change in velocity of the body.

iii) the acceleration of the body.

 iv) the distance travelled during the 4sec.

  v) the work done by the accelerating force.

 

44.a) Define the following terms:-

  i) uniform velocity

 ii) acceleration

iii) displacement

b) A man whose weight is 800N enters a lift. He stands on a weighing machine on the floor of the lift. What will the machine register when:-

  i) the lift is rising steadily at 3ms-1?

 ii) the lift is accelerating upwards at 1ms-2?

iii) the lift is accelerating downwards at 2ms-2?

c) A train of mass 100,000kg has an engine that hauls it with a steady force of 400,000N. How long will it take before the train reaches a speed of 50ms-1?

 

45.ai) Define momentum.

ii) State the law of conservation of momentum.

b) If a trolley of mass 2kg accelerates from rest to a speed of 5m/s in 10 seconds, calculate:-

 i) the increase in the kinetic energy of the trolley.

ii) the increase in the momentum of the trolley.

c) An object of mass 10kg is placed 45m above the ground.

 i) Calculate the potential energy of the object when it falls.

ii) Using the kinetic energy gained by the object when it reaches the bottom of the fall, calculate the maximum speed of the object.

 

46. A racing car starts from rest and moves with uniform acceleration of 3ms-2 for 5seconds. It then moves with uniform velocity for 3  seconds after which it is brought to rest again with a retardation of 4ms-2.

a) Draw a velocity-time graph of the motion of the car.

b) Find the time of retardation and the distance covered by the car.

 

47.ai) Define momentum of a body.

ii) State the law of conservation of momentum.

b) A bullet of mass 25g is fired with a speed of 300m/s from a rifle of 2.5kg. What is the initial recoil speed of the rifle?

c) A body of mass 20kg moving with uniform acceleration has an initial momentum of 200kgms-1 and after 10s, the momentum is 300kgms-1. What is the acceleration of the body?

d)           X                 Y                              Z

               .         .         .           .           .        .

 


                     6cm                   12cm

 

The figure shows a tape which was connected to a trolley. If the ticker-timer was vibrating at 40Hz,

 i) find the average velocity for portions XY and YZ.

ii) What was the acceleration of the trolley?

 

48.a) Define and give two examples of

 i) vector quantity

ii) scalar quantity

b) Determine the resultant force in the diagram below.

 

 


5N

 

 

 

        900                             10N

49.ai) Define the term velocity.

ii) Sketch the velocity-time graph for a body moving with uniform velocity.

b) Describe the motion of the body below:

 

 


                   20                    B                     C

Velocity

   (m/s)

 

 

                   10    A

 

 

                              

                        0                   5                 10                      15                   

 

c) Calculate the total distance covered.

 

50. When a heavenly body breaks up, the particles at first accelerate towards the center of the earth, then finally travel with a velocity known as “terminal velocity” until they reach the earth’s surface.

a) Name the three forces that act on the particles in the earth’s atmosphere.

b) Sketch a velocity-time graph representing the motion of the particles.

c) Explain what is meant by the term “terminal velocity”.

 

51. 2 trolleys A and B are on a rail so that A moves with velocity 6ms-1 and then collides with B and they both move with a mutual velocity. The mass of A is 5kg and of B is 3kg.

a) State the law of conservation of momentum.

b) State the law of conservation of energy.

c) What is the momentum of the two trolleys before collision?

d)What is the kinetic energy of the trolleys before collision?

 

52.ai) State Newton’s second law of motion.

ii) State the law of conservation of momentum.

b) A rocket of 4000kg is propelled by the steady force of its engine so that the velocity of the rocket 5 seconds after lifting off the ground is 50m/s.

  i) What is  the thrust of the engine?

 ii) How far will the rocket be 5 seconds after lifting off the ground?

iii) What is the momentum of the rocket 4 seconds after lifting off the ground?

 

 

 

 

 

 

 

53.

Velocity  m/s-1

         

           60  

 


          40

 

          20

 


                            2          4          6          8         10                           Time sec.

                           

a.i) What is the initial and final velocity of the body?

 ii) What time did it take to achieve the final velocity?

iii) What is the acceleration of the body?

 iv) Given that the body has a mass of 5kg, find the change in the kinetic energy.

  v) Use your change in K.E to find the distance travelled by the body through this change.

b) State Newton’s laws of motion.

c.i) What average net force is required to accelerate a car of mass 1200kg from rest to 20ms-1 in 10s?

ii) If an average braking force of 4800N is applied when the car is travelling at 20ms-1, how long will it take to stop the car?

 

54. A racing car starts from rest and moves with uniform acceleration of 3ms-2 for 4s. Then moves with uniform velocity for 2s and is brought to rest after a further 2s.

a) Draw a velocity-time graph of the motion of the car.

b) Find the total distance moved by the car.

 

55. A projectile is fired at an angle of 300 to the horizontal.

a) Draw a sketch of the path of the projectile.

b) n which direction is the force of acceleration acting on the projectile?

c) If the initial velocity of the projectile is 50m/s, what are its horizontal and vertical components?

 

56.a) State Newton’s first and 2nd laws of motion.

b) A trailer of mass 100kg is towed by means of a rope attached to a car. When the trailer and the car are moving at a steady velocity, the tension in the rope is 400N.Explain why the tension is not in zero.

c) When the car begins to accelerate, the tension in the rope is 1650N. What is the acceleration of the trailer?

 

57.a) Define the following terms as applied to motion.

  i) Acceleration

 ii) Velocity

iii) Displacement

b) A body starts moving with a velocity of 10ms-1, it accelerates uniformly to a velocity 30ms-1 in 6sec; it then moves at the velocity so attained for another 6sec. The body is then retarded uniformly to rest in another 6 sec.

i) Draw a diagram representing a velocity-time graph for the body showing the velocity and time at each stage of motion.

ii) Calculate the total distance travelled.

c) A body of mass 2kg is acted upon by three forces; 6N to its left, 10N to its right and 3N upwards. Find the magnitude of the acceleration with which the body moves.

 

58. A racing car starts from rest and moves with uniform acceleration of 3ms-2 for 5sec. Then moves with uniform velocity for 3sev after which it is brought to rest again by a retardation of 4ms-2.

a) Draw a velocity-time graph for the motion of the car.

b) Find the time of retardation and the total distance moved by the car.

 

59.a i) Define momentum.

ii) State the law of conservation of momentum.

b) An object A of mass 2kg is moving with a velocity of 3ms-1 and collides head on with an object B of mass 1kg moving in the opposite direction with a velocity of 4ms-1.

 

                    A  2kg                                            B  1kg

                                       

                                   3ms-1          4m-s        

 

 

After collision, both objects --------so that they move with a common velocity V.

 i) What type of collision is this?

ii) Calculate V.

c) A ball is projected horizontally from the top of a cliff 50m high. If it is given a horizontal velocity of 10m/s, find the horizontal distance from the cliff to the point where the ball hits the ground.

 

60.a) Define the following terms:-

  i) Displacement

 ii) Velocity

iii) Acceleration

b) A body of mass 4kg is moving initially at 10m/s. An accelerating force is applied to the body such that after a time of 4sec. Its velocity is 30m/s. Calculate:-

 i) The change in velocity of the body.

 ii) The acceleration of the body.

iii) The distance travelled during the 4s.

 iv) The workdone by the accelerating force.

c) A boy of mass 60kg jumps from a wall and lands on the ground at a speed of 5m/s.

  i) What is the momentum of the boy just before landing?

 ii) What is the change of momentum of the boy on landing?

iii) What is the rate of change of momentum if the boy takes 1.5sec. to land?

 iv) By considering your answers to (iii) explain why a higher jumper uses a thick mattress as a landing surface.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

REVISION  QUESTIONS

 

Motion

 

1.A)a TICKER-TIMER VIBRATES AT A FREQUENCY OF 50Hz. ThMOTION

 

1.a)A ticker-timer vibrates at a frequency of 50Hz. The distance between 2 dots is 4cm. Find;

  i)the time that elapses between two consecutive dots.

 ii)the average speed of the tape.

b)The ticker-timer ib (a) above was used to measure acceleration of a body which gave the following information.

Distance between 4th and 6th dot = 3cm

Distance between 6th and 8th dot = 7cm

What value was obtained for the acceleration?

 

2.A man who can swim at 3m/s in still water crosses a river which is flowing at 4m/s. He swims perpendicularly to the the flow of the river.

a)Sketch a diagram to show his resultant velocity.

b)if the river is 300m wide, how long will he take to cross it?

 

3.diag pp3

The tape above was produced by a ticker-timer vibrating at a frequency of 10Hz. The tape was being pulled bya trolley rolling down a slope.

  i)calculate the velocity in region A.

 ii)calculate the velocity in region B.

iii)find the change in velocity from region A to region B.

 iv)calculate the time taken to move from region A to B.

  v)calculate the acceleration of the trolley.

 

4.Use the questions  above in all the cases below.

a)diag pp3

The above tape was produced by a ticker-timer vibrating at a frequency of 50Hz.

b)diag pp3

The above tape was produced by a ticker-timer vibrating at a frequency of 20Hz.

c)diag pp3

The above tape was produced by a ticker-timer vibrating at a frequency of 50Hz.

 

5.The diagram shows two sections of one tape obtained from a ticker-timer experiment.diag pp3

  i)calculate the average velocity of the trolley between dots P and Q and R and S.

 ii)calculate the acceleration of the trolley.

iii)what force was applied to this trolley of mass 100g to give this much accelaration.

 

6.A stone is thrown with a horizontal velocity of 50ms-1 from the top of a cliff. It takes 4seconds to land. Find;

  i)the height of the cliff.

 ii)the horizontal distance travelled on landing.

iii)the vertical velocity attained on landing.

 iv)the horizontal velocity on landing.

 

7.A boy playing football on a shade at the top of a building kicks the ball and it leaves the shade with a horizontal speed of 30ms-1. If it falls through a horizontal distance of 150m on landing, find;

  i)the time the ball takes to land.

 ii)the height of the building.

iii)the vertical velocity of the ball on landing.

 

8.Calculate the velocity of a ball after 4s if it is initially travelling vertically downwards at 5ms-1.

 

9.A boulder is sliding down a slope with a uniform accelerationof 3ms-2. If its starting velocity was 2ms-1, calculate its velocity after it has slid 10m down the slope.

 

10.A motor car is uniformly decelerated from 90kmh-1 to 18kmh-1 in a time of 10s. Calculate the acceleration.

 

11.A rocket is uniformly accelerated from rest to a speed of 960ms-1 in 1 2/3 minutes. Calculate the distance travelled.

 

12.State Newton’s laws of motion.

A block of wood of mass 245g is sent sliding along a rough horizontal table, the initial speed being 3m/s. If the resistance to motion is 0.5N, find the distance travelled and the time taken before the block comes to rest.

 

13.A projectile of mass 200g moving at 400m/s hits a movable target of mass 10kg which is at rest. The target and projectile move on together after the impact. Find;

 i)the initial momentum of the projectile.

ii)the combined velocity just after the impact.

 

14.A bullet of mass 100g moving at 100m/s becomes embedded in a stationary suspended target of mass 10kg. What is their combined velocity just after impact?

 

15.A truck of mass 900kg moving at 8m/s collides with a truck of mass 1000kg moving in the same direction at 5m/s. If they move on together, what is their combined velocity just after the collision?

 

16.A 10kg projectile leaves a 1200kg launcher with a velocity of 500m/s forward. What is the recoil velocity of the launcher?

17.A large space rocket has motors which eject 11,000kg of propellant per second with a velocity of 3000m/s. What thrst does this produce?

 

18.A man of mass 100kg stands on a weighing machine in a lift. The lift moves upward with an acceleration of 0.6m/s2 for a short time and after moving with constant velocity for a brief period, is brought to rest with a retardation of 1.0m/s. Find the reading of the weighing machine during the three phases of the motion.

(i.e upward acceleration, constant velocity, retardation).

Projectiles:

19.A stone is thrown horizontally from the edge of a cliff 40m above the sea. Given that the stone travels 60m horizontally before it hits the water, find;

 i)the time for which it is in the air and its initial speed.

ii)the velocity of the stone as it hits the water.

 

Ticker-Timer

20.Find the acceleration of the trolley tape below if the timer is vibrating at 50Hz.diag pp5

 

21.The piece of tape below was made with a ticker-timer vibrating at 40Hz. What was the acceleration of the trolley?diag pp5

 

22.If the trolley is vibrating at 10Hz, find the acceleration of the trolley from the tape below.diag pp5

 

23.diag pp5

If the tape above is from a timer vibrating at 50Hz. Find the acceleration of the trolley.

 

24.A ticker-timer vibrates at a frequency of 10Hz. The distance between two consecutive dots is 3cm and the distance between the 4th and 5th dots is 4cm, calculate the acceleration of the tape.

 

25.The diagram below shows dots produced on a tape pulled through a ticker-timer by a moving body. The frequency of the ticker-timer is 50Hz.

Diag pp6

Calculate the acceleration of the body.

 

26.A car starting from rest accelerates at a rate of 2ms-2 for 20seconds,it moves at constant velocity for 20seconds before uniformly brought to rest in 8 seconds.

a)Draw a sketch graph of velocity against time for the motion.

 

27.a)What is the difference between speed and velocity?

b)The graph shows the variation of distance with time for a body. Describe the motion of the body.

Diag pp8

c)Describe an experiment to demonstrate friction compensation using an inclined plane.

 

28.a)Distinguish between speed and velocity.

b)A ball is thrown vertically upwards. Sketch graphs which represent;

 i)the variation of velocity of the ball with time.

ii)the distance travelled by the ball against time.

c)A stone was projected horizontally at 20ms-1 from the top of a building 30m high;

 i)Name the path traced by the stone.

ii)What horizontal distance is covered by the stone from the bottom of the building?

d)i)State the principle of conservation of momentum.

 ii)What is meant by an elastic collision?

iii)A 2kg steel ball moving at 4ms-1 collides head-on with another of mass 1.5kg moving at 3ms-1 both on a horizontal smooth surface. If an inelastic collision occurred, determine their velocity after collision.

 

29.a)What is meant by the following terms;

i)Velocity       ii)Acceleration

b)An object of mass 2kg is moving with a velocity of 1ms-1. It is then acted upon by a force of 5N through a distance of 16m. Calculate;

  i)the acceleration produced by the force.

 ii)the final velocity of the object.

iii)the work done by the force.

c)State the principle of conservation of momentum.

d)A trolley of mass 3kg moving at 8m/s collides head on with another trolley of mass 2kg moving at 4m/s in the opposite direction. The trolleys move together after collision.

 i)What type of collision is this?

ii)Determine the common velocity after collision.

 

30.a)Define acceleration.

b)A body of mass 4kg is pulled along a smooth horizontal bench by a string which passes over a pulley and carries a 2kg mass on its other end.

Diag pp11

Find the acceleration of the system and the tension in the string.

 

31.a)What do you understand by the term “uniformly accelerated body”?

b)A body moves with constant acceleration for 5s starting with a velocity of 3ms-1. It then moves with uniform velocity for 8s after which is non-uniformly retarted for further 2s to come to rest.

 i)Sketch a velocity/time graph for the motion.

ii)Find the distance covered by the first 5 seconds.

 

32.a)What is meant by kinetic energy and potential energy?

b)diag pp13

A ball of mass 100g falls from rest through a height of 2m onto the top of a spring of length 1m, placed on a table as shown in figure 2 above.

 i)How much energy is passed on to the spring by the ball?

ii)If the elstic constant of the spring is 100Nm-1, what will be the compression in the spring?

 

33.a)A car is uniformly accelerated from a velocity of 8ms-1 at a rate of 3ms-2for 5s. The brakes are then suddenly applied and the car comes to rest in a further 7s.

  i)sketch a velocity-time graph for the motion.

 ii)Calculate the maximum velocity attained.

iii)Find the total distance covered.

 iv)What could be the possible reason for this sudden braking?

  v)What caused the car to stop?

b)A girl throws a stone horizontally from the edge of a cliff into a lake to hit a fish at a velocity of 25ms-1. It strikes the water surface at a distance of 80m from the base of the cliff. Determine the height of the cliff.

c)Food parcels to be dropped from an aeroplane flying horizontally, have to be released a little before the plane is vertically above a relief camp. Explain this observation.

 

34.a)Define the following terms;

  i)Velocity

 ii)Acceleration

iii)Momentum

 iv)Displacement

b)Sketch displacement-time graphs for a body;

  i)with uniform velocity.

 ii)uniform acceleration

iii)at rest.

 iv)increasing acceleration.

c)A car starts from rest and is accelerated uniformly at 2.4m/s2 for 25 seconds. It moves with the velocity thus attained for 5 minutes and then accelerated again  at 1.3m/s2 for 6 seconds. It is then brought to rest with uniform retardation in another 8 seconds.

 i)sketch a velocity-time graph for the motion of the car.

ii)calculate the maximum velocity attained, the total distance moved and the average velocity.

 

35.ai)Define the terms velocity and reaction time.

ii)A steel ball-bearing is released from rest and let to fall through a tall jar with filled with oil. Sketch a velocity-time graph for the motion.

b)A car travelling at a velocity of 10m/s is uniformly accelerated at a rate of 3m/s2 for 5s. It then moves at the maximum speed attained for 8s. The driver then sees a school girl crossing the road. He applies the brakes bringing the car to rest in 2s.

 i)Sketch the velocity-time graph.

ii)calculate the total distance covered.

c)An object of mass 4kg is dropped from a height of 100m from a helicopter. The air resistance acting against the paracute exerts a steady upwards force of 35N. Calculate the kinetic energy of the object when it reaches the ground.

 

36.a)State Newton’s law of motion.

b)A minibus of mass 576kg can accelerate from rest to 72Kmh-1 in 20s. If the acceleration is assumed uniform, find this acceleration and the tractive force in Newtons needed to produce it.

c)A mass of 2kg projected along a flat surface with a velocity of 15ms-1 comes to rest after travelling 30m. What is the frictional force?

 

37.a)State the law of conservation of momentum.

b)diag pp19

In the figure above, spheres A and B are resting on a smooth surface. A has a mass of 2Kg and is projected towards B of mass 3Kg with a velocity of 10m/s. It collides and gets stuck to B so that they move together. Find the common velocity.

 

38.A falling body pulls a length of paper tape through a stationary vibrator which prints 50 dots on the tape each second.

a)What time does it take the vibrator to print 10 dots?

b)If the distance from  the 10th to the 20th dot is 30cm and that from the 20th to the 30th is 50cm, calculate the acceleration of the tape.

 

39.An object of mass 2Kg is moving with a velocity of 1ms-1. It is then acted upon by a force of 5N through a distance of 16m.

Calculate:-

a)the acceleration produced by the force.

b)the final velocity of the object.

c)the work done by the force.

 

40.a)Define acceleration.

b)A car of mass 1000Kg was moving at 80Kmh-1 when its engine is switched off. If a constant frictional force of 2500N acts on the car, how long will it be before the car stops from the time the engine is switched off?

 

41.a)Define the following:-

 i)Displacement    ii)Momentum

b)Sketch graphs of velocity-time for a body moving with;

 i)zero acceleration

ii)acceleration which increases with time.

c)A body of mass 4kg is moving initially at 10m/s. An accelerating force is applied to the body such that after a time of 4seconds, its velocity is 30m/s. Sketch the velocity-time graph and calculate:-

  i)the change in velocity of the body.

 ii)the distance travelled during the 4seconds.

iii)the acceleration of the body.

 iv)the work done by the acceleratong force.

 

 

42.a)What is momentum?

b)State the law of conservation of momentum.

c)A bullet of mass 20g is fired with a speed of 250m/s from a rifle of mass 2.0kg. What is the initial recoil speed in m/s of the rifle?

 

43.a)Define the following terms as applied to motion:-

  i)displacement

 ii)velocity

iii)momentum

b)a body of mass 4kg is moving initially at 10m/s. An accelerating force is applied to the body such that after 4sec. Its velocity is 30m/s.

  i)Sketch the velocity-time graph for this motion.

Calculate:-

 ii)the change in velocity of the body.

iii)the acceleration of the body.

 iv)the distance travelled during the 4sec.

  v)the work done by the accelerating force.

 

44.a)Define the following terms:-

  i)uniform velocity

 ii)acceleration

iii)displacement

b)A man whose weight is 800N enters a lift. He stands on a weighing machine on the floor of the lift. What will the machine register when:-

  i)the lift is rising steadily at

3ms-1?

 ii)the lift is accelerating upwards at 1ms-2?

iii)the lift is accelerating downwards at 2ms-2?

c)A train of mass 100,000kg has an engine that hauls it with a steady force of 400,000N. How long will it take before the train reaches a speed of 50ms-1?

 

45.ai)Define momentum.

ii)State the law of conservation of momentum.

b)If a trolley of mass 2kg accelerates from rest to a speed of 5m/s in 10 seconds, calculate:-

 i)the increase in the kinetic energy of the trolley.

ii)the increase in the momentum of the trolley.

c)An object of mass 10kg is placed 45m above the ground.

 i)Calculate the potential energy of the object when it falls.

ii)Using the kinetic energy gained by the object when it reaches the bottom of the fall, calculate the maximum speed of the object.

 

46.A racing car starts from rest and moves with uniform acceleration of 3ms-2 for 5seconds. It then moves with uniform velocity for 3  seconds after which it is brought to rest again with a retardation of 4ms-2.

a)Draw a velocity-time graph of the motion of the car.

b)Find the time of retardation and the distance covered by the car.

 

47.ai)Define momentum of a body.

ii)State the law of conservation of momentum.

b)A bullet of mass 25g is fired with a speeed of 300m/s from a rifle of 2.5kg. What is the initial recoil speed of the rifle?

c)A body of mass 20kg moving with uniform acceleration has an initial momentum of 200kgms-1 and after 10s, the momentum is 300kgms-1. What is the acceleration of the body?

d)diag pp30

The figure shows a tape which was connected to a trolley. If the ticker-timer was vibrating at 40Hz,

 i)find the average velocity for portions XY and YZ.

ii)What was the acceleration of the trolley?

 

48.a)Define and give two examples of

 i)vector quantity

ii)scaler quantity

b)Determine the resultant force in the diagram below.

Diag pp31

 

49.ai)Define the term velocity.

ii)Sketch the velocity-time graph for a body moving with uniform velocity.

b)Describe the motion of the body below:

diag pp31

c)Calculate the total distance covered.

 

50.When a heavenly body breaks up, the particles at first accelerate towards the center of the earth, then finally travel with a velocity known as “terminal velocity” until they reach the earth’s surface.

a)Name the three forces that act on the particles in the earth’s atmosphere.

b)Sketch a velocity-time graph representing the motion of the particles.

c)Explain what is meent by the term “terminal velocity”.

 

51.2 trolleys A and B are on a rail so that A moves with velocity 6ms-1 and then collides with B and they both move with a mutual velocity. The mass of A is 5kg and of B is 3kg.

a)State the law of conservation of momentum.

b)State the law of conservation of energy.

c)What is the momentum of the two trolleys before collision?

d)What is the kinetic energy of the trolleys before collision?If the law of conservation of momentum is obeyed,

e)What is their momentum after collision?

f)What is their mutual kinetic energy?

 

 

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