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 1-2^{nd}, s =
__15__m/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
=(__1__x5x50) + (__1__x5x-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 1^{st} 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
+ __1__at2

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/s^{2}

s
= ut + __1__ at^{2}

2

= 0 x 4 x__1__x 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/s^{2}

^{
}t =
10
u =12m/s

u = 12
a = -9.8m/s

s = ut + __1__at^{2
}120 + 490 =

^{
}2

= -12.10 + __1__.9.8.10^{2
}t = 10s

2

= -120 + 490
s = ut + __1__at^{2}

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
2^{nd} 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 10^{6}kg moving at 5m/s

c)
an
electron of mass 9 x 10^{-31}kg moving at 2
x10^{7}m/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 __ =
__3000__v

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
10^{6}Ns.

Reaction
force onto the rocket = 33 x 10^{6}Ns = F,

F = 3.3 x 10^{6}N

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 4^{th} and 6^{th} dot = 3cm

Distance
between 6^{th} and 8^{th} 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.
. . . . . . . . . . . . .
.

X_{1} cm
X_{2}cm

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 4^{th} and
5^{th} 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/s^{2} for 25
seconds. It moves with the velocity thus attained for 5 minutes and then
accelerated again at
1.3m/s^{2} 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/s^{2} 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
10^{th} to the 20^{th} dot is 30cm and that from the
20^{th} to the 30^{th} 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

90^{0
} 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 30^{0} 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 2^{nd} 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 4^{th} and 6^{th} dot = 3cm

Distance
between 6^{th} and 8^{th} 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 4^{th} and
5^{th} 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
10^{th} to the 20^{th} dot is 30cm and that from the
20^{th} to the 30^{th} 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?