Equations of Uniform
Accelerated Motion
AP Physics C
Mrs. 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= Dx = x-xo
More
Equations vavg = ½ (vo +v)
of Motion
for Uniform
Dx = ½ (vo+ v)t
Accelerated
Motion
Assume that ti=0
Example of Position vs Time
(Positive Acceleration)
Position x= xo + vot + ½ at2
(m)
Parabola
o
Time (s)
Slope of Tangent at a given time=
Instantaneous Velocity at that time
Example of Velocity vs Time
(Positive Acceleration)
Velocity v= vo+ at
(m/s)
o
Time (s)
Slope of Line= Acceleration
Area Under Line=Displacement
Example of Acceleration vs Time
(Const. a)
Acceleration
(m/s2)
o
Time (s)
Area under line = Change in Velocity
How do we derive Dx = ½ (vo+ v)t
from the graph?
v
Velocity
(m/s)
vo
o
t Time (s)
Hint: Area Under the Line=Displacement Δx
Example of Position vs Time
(Negative Acceleration)
Position
(m) Parabola
o
Time (s)
Example of Velocity vs Time
(Negative Acceleration)
Velocity
(m/s)
o
Time (s)
Slope of Line= Acceleration
Area Under Line=Displacement
Example of Acceleration vs Time
(Negative a)
Acceleration
(m/s2)
o
Time (s)
Area under line = Change in Velocity
How do we derive x= xo + vot + ½ at2 ?
Hint: Start with Dx = 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 Dx = 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