1. Constant acceleration
Constant velocity
Constant acceleration
a, m/s2
t, s
v, m/s
x, m
a, m/s2
t, s
v, m/s
x, m

2. constant acceleration
Position vs Time
constant acceleration
x, m
t, s
0.5
1.0
1.5
2.0
2.5 1 2 3 4 5 6
x~t2 ?

3. Velocity vs Time Displacement?
Use the graph to find the object’s displacement from 0sec to 2sec
v, m/s 6 5 4 3
Use the graph to find the object’s displacement from 0sec to 4sec 2 1 1 2 3 4 5
t, s
Use the graph to find the object’s displacement from 2sec to 5sec

4. Velocity vs Time 9 meters Displacement? t, s v, m/s 6 5 4 3 2 1 1 2 31 2 3 4 5
t, s

5. Velocity vs Time 15 meters Displacement? t, s v, m/s 1 2 3 4 5 6 1 2 31 2 3 4 5
t, s

6. Velocity vs Time 13.75 meters Displacement? t, s v, m/s 6 5 4 3 2 1 11 2 3 4 5
t, s

7. Velocity vs Time 12.5 meters Displacement? t, s v, m/s 1 2 3 4 5 6 1 21 2 3 4 5
t, s

8. Velocity vs Time
Displacement?
v=at
v, m/s 5a ? ? 1 2 3 4 5
t, s

9. Velocity vs Time v=at X = ½ at2 aT 5a ½ 25a ½ aT2 T t, s t, s v, m/s1 2 3 4 5 T
t, s
x, m
t, s
0.5
1.0
1.5
2.0
2.5 1 2 3 4 5 6

10. vf - vi = at x = vit + ½ at2 vf X2 = ½ (vf – vi)T X2 = ½ aT2 X1 = viT
acceleration =
change in velocity
time
vf - vi = at
v, m/s vf
X2 = ½ (vf – vi)T X2
= ½ aT2
X1 = viT X1 vi
X = X1 + X2 = viT + ½ aT2 T
t, s
x = vit + ½ at2
Check the units!
Check the limiting cases!
Xtrain + Xboy a
vi = const

11. vf - vi = aT vf X2 X2 = ½ (vf – vi)T X1 X1 = viT vi
acceleration =
change in velocity
time
v, m/s
vf - vi = aT vf X2
X2 = ½ (vf – vi)T X1
X1 = viT vi
X = X1 + X2 =vi T + ½ (vf – vi)T
X = ½ (vf + vi)T
T = (vf-vi)/a T
t, s
X =
(vf2– vi2) 2a
a≠0!
Check the units!
Check the limiting cases!
2aX = (vf2– vi2)

12. A ball is thrown straight up. At the top of its trajectory, its
velocity is zero, acceleration is zero.
velocity is non-zero, acceleration is non-zero.
velocity is zero, acceleration is non-zero.
velocity is non-zero, acceleration is zero.

13. This graph shows velocity as a function of time for a car of mass 1
This graph shows velocity as a function of time for a car of mass 1.5 x 103 kg. What was the acceleration at the 90 s mark?
(A) 0.22 m/s2
(B) 0.33 m/s2
(C) 1.0 m/s2
(D) 9.8 m/s2
(E) 20 m/s2

14. Homework (due Friday) Problems
Section D Motion with Constant Acceleration (p.50)
#30, 39, 40

15. Quiz
A stone is thrown straight upward with an initial velocity v0. Sketch graphs:
(a) acceleration versus time
(b) velocity versus time
(c) position versus time.