1. Calculating Acceleration
Unit 9.2

2. m/s2
average acceleration

3. Dv Dt
a =
50 m/s – 25m/s =
4s – 2s =
12.5 m/s2

4. B C A A C
none B

5. nf – ni
tf – ti

6. Practice: A pool ball travelling at 2
Practice: A pool ball travelling at 2.5 m/s towards the cushion bounces off at 1.5 m/s. If the ball was in contact with the cushion for 0.20 s, what is the ball’s acceleration? (Assume towards the cushion is the positive direction.)
= - 20 m/s2

7. Dv vf - vi Dt Dt a = = vf = aDt + vi = (3.0m/s2)(5.0s) + 0m/s
Practice: A car accelerates from rest at 3.0 m/s2 forward for 5.0 s. What is the velocity of the car at the end of 5.0 s?
Dv vf - vi
Dt Dt
a = =
vf =
aDt + vi
vi = 0 m/s
Dt = 5.0s
a = 3.0 m/s2
vf = ?
= (3.0m/s2)(5.0s) + 0m/s
= 15 m/s [forward]

8. Dv vf - vi Dt Dt a = = Dt = vf - vi a = -22m/s – (-14m/s) -0.50m/s2
Practice: A train is travelling west at 14 m/s. How long would to increase its velocity to 22 m/s west, if it accelerated at 0.50 m/s2 west? Assign east direction positive (+).
Dv vf - vi
Dt Dt
a = =
Dt =
vf - vi a
= -22m/s – (-14m/s)
-0.50m/s2
vi = -14 m/s
vf = -22 m/s
a = m/s2
Dt = ?
= 16 s

9. Dv vf - vi Dt Dt a = = = -18m/s – 0 m/s 4.5 s = - 4 m/s2 vi = 0 m/s
Practice: Solve the following problems.
A truck starting from rest accelerates uniformly to 18 m/s [W] in 4.5 s. What is the truck’s acceleration?
Dv vf - vi
Dt Dt
vi = 0 m/s
vf = -18 m/s
Dt = 4.5 s
a = ?
a = =
= -18m/s – 0 m/s
4.5 s
= - 4 m/s2

10. Dv vf - vi Dt Dt a = = vf = aDt + vi = (-0.40m/s2)(10s) + 5m/s = 1 m/s
Practice: Solve the following problems.
A toboggan moving 5.0 m/s forward decelerates backward at m/s2 for 10 s. What is the toboggan’s velocity at the end of the 10 s?
vi = 5 m/s
a = m/s2
Dt = 10 s
vf = ?
Dv vf - vi
Dt Dt
a = =
vf =
aDt + vi
= (-0.40m/s2)(10s) + 5m/s
= 1 m/s

11. Dv vf - vi Dt Dt a = = Dt = vf - vi a = -26m/s – (-12m/s) -3.5m/s2
Practice: Solve the following problems.
How much time does it take a car travelling south at 12 m/s to increase its velocity to 26 m/s south if it accelerates at 3.5 m/s2 south?
Dv vf - vi
Dt Dt
a = =
Dt = ?
vi = -12 m/s
vf = -26 m/s
a = -3.5 m/s2
Dt =
vf - vi a
= -26m/s – (-12m/s)
-3.5m/s2
= 4 s

12. Air resistance
same rate
9.8 m/s2
-9.8 m/s2

14. decreasing increasing -9.8 m/s2 -9.8 m/s2 -9.8 m/s2 A → B B B → C
Velocity
Acceleration
decreasing
increasing
-9.8 m/s2
-9.8 m/s2
-9.8 m/s2

15. Practice: Solve the following problems.
Suppose a rock falls from the top of a cliff. What is the change in velocity of the rock after it has fallen for 1.5 s? Assign “down” as negative (-).
What is the change in velocity of a brick that falls for 3.5 s?

16. Practice: Solve the following problems.
A ball is thrown straight up into the air at 14 m/s. How long does it take for the ball to slow down to an upward velocity of 6.0 m/s?
A rock is thrown downwards with an initial velocity of 8.0 m/s. What is the velocity of the rock after 1.5 s?