Kinematics

Motion

• Change in position of object in relation to things that are considered stationary
• Nothing is truly stationary
• All motion is relative: must be related to other objects called your frame of reference
• Usually earth is considered stationary

Distance and Displacement

• Distance: scalar quantity, how far object moves without respect to direction
• Displacement: a vector quantity, change of position in a particular direction; how far and in what direction object is from original position
• Both use symbol d (sometimes s), and unit of meter

Speed

• The time rate of motion; the rate of change of position; a scalar
• Units of distance / time; m/s usually but can be miles/hr, km/hr; symbol is v
• Average speed = total distance / elapsed time
• Instantaneous speed: rate of change of postion at any instant

Velocity

• Speed in a particular direction, a vector; unit same as speed; symbol v
• Must include a direction, using angle from known reference points, compass headings, or sometimes just left, right, back, etc.
• Can be negative (going backwards)
• Average velocity = total displacement / elapsed time
• Instantaneous velocity: instantaneous speed with current direction
• Constant velocity means no change of speed or direction
• Often we are interested in only the speed (we may know the direction) so the terms are often used interchangeably

Graphing Motion

• On displacement vs. time graph, slope at any value of t gives instantaneous v
• If d vs t graph is linear, slope and v are constant
• If graph is curved, slope and v are found by drawing tangent line to curve and finding its slope

Acceleration

• Time rate of change of velocity; a vector; symbol a and units of m/s/s usually shortened to m/s²
• Acceleration can be negative (deceleration)
• Average acceleration = change in velocity / elapsed time for the change
• Galileo first to understand acceleration

Graphs with Acceleration

• On v vs t graph, acceleration is slope
• If graph is linear, acceleration is constant
• If graph is curved, instantaneous acceleration is found using slope of tangent line at any point

1st Constant Acceleration Equation

• If acceleration is constant, instantaneous acceleration always equals avg acceleration
• Use definitions of avg velocity and accel to calculate final velocity or distance
• since a = (v_f - v_i)/t , then v_f = v_i + at
• If v_i = 0 , then v_f = at
• Use when distance not given or asked for

2nd Constant Acceleration Equation

• v_avg = (v_f + v_i)/2 ; but also v_avg = d/t ; so (v_f + v_i)/2 = d/t
• Now using our first equation for v_f we can get (v_i + v_i + at)/2 = d/t
• Solving for d: d = v_it + ½at²
• If v_i = 0, d = ½at²
• Use when final speed not given or asked for

3rd Constant Acceleration Equation

• Solve 1st equation for t and substitute into 2nd equation, expand squared quantity and combine terms.
• Get 2 ad = v_f ²- v_i2; solve for v_f ²
• v_f²= v_i² + 2ad
• If v_i = 0, v_f²= 2ad
• Use when time is not given or asked for

Free Fall

• Common situation for constant acceleration is free fall
• Force of gravity causes falling bodies to accelerate
• Force varies slightly from place to place but average acceleration is 9.80 m/s²
• Use symbol g to designate accel due to gravity
• Can use all constant acceleration equations for free fall.
• Usually are written with symbol g in place of a in equations
• Since motion is vertical, up and down, being in opposite directions, must have opposite signs