Acceleration Unit Review
1. A car covers 2.5 km in 70 s starting from rest. Find its final velocity and acceleration.
2. Find the acceleration of a car covering 400 m while speeding up steadily from 20 m/s to 30 m/s.
3. A car is coasting down a hill backwards at 3.0 m/s when the driver gets his engine started. It then accelerates steadily until, 3 seconds later, it is going 4.5 m/s up hill. Find the acceleration.
4. A bus is moving 40 km/h when the driver applies the brakes, and it stops in 3.0 seconds. What was the acceleration and the stopping distance?
5. A golf-ball rolls up a hill towards a mini-golf hole starting at 2.0 m/s. It misses the hole and continuously accelerates at – 0.5 m/s2 until it reaches its original position again and the golfer stops it.
a) What is the velocity of the ball 1.5 seconds after it starts?
b) What is the velocity of the ball 3.6 seconds later?
c) What it the maximum distance between the ball and the starting point?
d) At what time(s) is the ball 1.3 m from the starting point?
6. A car slows uniformly from 44 m/s to 22 m/s over a 9 second interval.
a) How far does it travel?
b) What is the acceleration?
7. A car accelerates uniformly from 30 km/h to 40 km/h in 6.5 seconds and then carries on at 40 km/h for an additional 10 seconds. Find the total distance travelled.
8. A car accelerates from rest for 10 s at 3.5 m/s2, and then decelerates to rest at -2.5 m/s2. Find the total time taken and the total displacement.
9. A car on an icy surface needs 50 m to stop from an initial speed of 30 km/h. Find a stopping distance for the same car on the same surface if its initial speed is
a) 60 km/h
b) 90 km/h
10. How far does a rock fall if it is dropped from rest and falls for 2.5 seconds?
11. You throw a ball upwards from ground level at 23 m/s.
a) What is the velocity after 2.0 seconds?
b) What is the velocity after 4.0 seconds?
c) How high is the ball when its velocity is 13 m/s?
d) When is the ball at a height of 2.5 m?
12. A physics student drops a rock from a high cliff and 5.3 seconds later hears it hit bottom. Assuming that the time needed for the sound to travel is negligible, what is the height of the cliff?
13. Assuming the above graph is a displacement (meters) vs. time graph:
a) What is the velocity at 2 seconds?
b) What is the velocity at 4 seconds?
c) What is the velocity at 7 seconds?
d) What is the acceleration at 5 seconds?
e) What is the average velocity?
f) At what times is the object at rest?
g) Draw a velocity vs. time graph for the same motion.
14. Assuming the above graph shows velocity (m/s) vs. time:
a) When is the object at rest?
b) When is the object moving at a constant velocity?
c) What is the velocity at 4 seconds?
d) What is the acceleration at 1.3 seconds?
e) What is the acceleration at 2 seconds?
f) What is the acceleration at 11.7 seconds?
g) What is the displacement in the first 2 seconds?
h) What is the total displacement?
i) What is the average velocity?
j) What is the average velocity during the 5th second?
k) Draw a displacement vs. time graph for the same motion.
15. A bright green smart car is driven (horizontally) off a cliff at a speed of 72 km/h.
a) If the cliff is 57 m high, how far from the base of the cliff does the car land?
b) Find the velocity of the car 1.5 seconds after it leaves the cliff.
c) Find the speed of the car just before it hits the ground.
d) How far away from the cliff is the car when it is 12 m above the ground?
e) At what time is the speed of the car 22 m/s?
16. An arrow is fired straight up and reaches a maximum height of 123 m. Find
a) the initial velocity.
b) the velocity after 2.5 seconds.
c) the time at which the arrow is moving down at 13 m/s.
d) the total time in the air.
17. A tractor is driven off a cliff at 39 m/s. It lands 141 m from the base. Find
a) the height of the cliff.
b) the velocity at impact.
c) the velocity 1.5 seconds after it leaves the cliff edge.
d) when the speed through the air is 45 m/s.
Answers
1. 71 m/s, 1.0 m/s2
2. 0.63 m/s2
3. 2.5 m/s2
4. -3.7 m/s2, 17 m
5. a) 1.2 m/s, b) 0.20 m/s, c) 4.0 m, d) 7.3 s and 0.71 s
6. a) 300 m, b) -2.4 m/s2
7. 170 m
8. 420 m, 24 s
9. a) 200 m, b) 450 m
10. 31 m
11. a) 3.4 m/s, b) -16 m/s, c) 18.4 m, d) 0.11 s and 4.6 s
12. 140 m
13. a) 2.5 m/s,b) 2.5 m/s, c) 0, d) 0, e) 1.25 m/s, f) 6 to 12 s,
g)
14. a) 2 s, b) 6 to 12 s, c) 5 m/s, d) 2.5 m/s2, e) 2.5 m/s2, f) 0, g) -5 m, h) 75 m,
i) 6.25 m/s, j) 6.25 m/s, k)
15.a) 68.2 m, b) 24.8 m/s at 36° with the horizontal, c) 39 m/s, d) 61 m, e) 0.935 s
16. a)49.1m/s, b)24.6m/s, c)6.3s, d)10s
17. a)64m, b)53 m/s at 42° with the horizontal, c)42 m/s at 21° with the horizontal,
d)2.3s