Equations of Uniform Accelerated Motion

AP Physics CMrs. Coyle

Uniform Accelerated Motion

Motion with constant acceleration Straight line Same direction

Equations for Uniform Accelerated Motion Velocity v= vo+ at

Position x= xo + vot + ½ at2

v2 = vo2 + 2a(x-xo)

Remember:

Displacement= x = x-xo

MoreEquations of Motion for Uniform Accelerated Motion

vavg = ½ (vo +v)

x = ½ (vo+ v)t

Assume that ti=0

Example of Position vs Time (Positive Acceleration)

Time (s)

o

Position (m)

Parabola

Slope of Tangent at a given time= Instantaneous Velocity at that time

x= xo + vot + ½ at2

Example of Velocity vs Time (Positive Acceleration)

Time (s)o

Velocity (m/s)

Slope of Line= Acceleration

Area Under Line=Displacement

v= vo+ at

Example of Acceleration vs Time (Const. a)

Time (s)

o

Acceleration (m/s2)

Area under line = Change in Velocity

How do we derive x = ½ (vo+ v)t from the graph?

Time (s)o

Velocity (m/s)

Hint: Area Under the Line=Displacement Δx

v

vo

t

Example of Position vs Time (Negative Acceleration)

Time (s)

o

Position (m) Parabola

Example of Velocity vs Time (Negative Acceleration)

Time (s)o

Velocity (m/s)

Slope of Line= Acceleration

Area Under Line=Displacement

Example of Acceleration vs Time (Negative a)

Time (s)

o

Acceleration (m/s2)

Area under line = Change in Velocity

How do we derive x= xo + vot + ½ at2 ?

Hint: Start with x = ½ (vo+ v)t

and then substitute for v that v = vo+at.

How do we derive v2 = vo2 +

2a(x-xo)?

Hint: Start with x = ½ (vo+ v)t

then substitute for t = (v – vo) /a

Problem 1

A ball initially stationary, accelerates at 0.25m/s2 down a 2m inclined plane. It then rolls up another incline, where it comes to rest after rolling up 1m.

a) What is the speed of the ball at the bottom of the incline and how much time did this take?

b) What is the acceleration along the second plane?

Answer: a) 1m/s, 4sec, b) -0.5m/s2

Problem 2 A Mustang travelling with a constant velocity

of 35m/s, passes a stationary police car.

The reaction time of the officer was 2.5sec and he then accelerates at 5.0 m/s2 to catch the Mustang. How long does it take for the police car to catch the Mustang?

 

Answer: 15.8sec