Equations of Motion
1. A landing module is falling towards the Moon’s surface at a steady speed of 500 ms−1. At a height of 62.5
m, a small object becomes detached from the landing module and accelerates down with the acceleration
of 1.60 ms−2. At what speed does the object hit the surface of the moon?
[3]
2. A car slows down from a velocity of 22 ms−1 to 5.0 ms−1 in a period of 6.0 s. For this car, calculate:
a) its deceleration
[3]
b) its average velocity
[1]
c) the distance travelled in 6.0 s.
[2]
3. A painter accidentally drops a can of paint from a bridge over a river. The can acceleration at 9.81 ms−2
for a time of 2.3 s before it hits the water below.
a) Calculate the velocity of the can just before it hits the water.
b) What is the height of the bridge?
[3]
[3]
4. A cyclist is travelling at a constant velocity of 4.0 ms−1. She suddenly accelerates at 0.45 m s−2 for a
distance of 9.0 m. Calculate her final velocity.
[3]
5. A racing car travelling at a velocity of 45 ms−1 hits a safety barrier. The car comes to a halt after
travelling a distance of 20 m. Calculate the average deceleration of the car. [3]
Motion under Gravity [Gravity = 9.81ms-2]
6. A rock is dropped from a height of 20m
a) How long does it take to reach the floor?
b) What is the velocity of the rock when it hits the floor?
7. Smith throws a ball into the air at an initial velocity of 10m/s
a) How long does it take for the ball to return to its starting position? b) How high does the ball travel?
8. A stone is dropped from the top of a tower which is 20m high. How long does it take the stone to reach
the ground?
9. A book is dropped from the top of a tower. It hits the ground with a speed of 15m/s. By
modelling the
book as a particle, find the height of the tower.
10. A stone is catapulted vertically upwards with a velocity of 25m/s from a point 2m above the ground.
Find:
(a) Its velocity when it hits the ground.
(b) The time it takes to reach the ground.
11. Water from a fountain rises to a height of 6m. By modelling the drops as particles, find the speed of the
water as it leaves the nozzle.
12. A ball is thrown vertically upwards with a speed of 29m/s. It hits the ground 6 seconds later. By
modelling the ball as a particle, find the height above the ground from which it was thrown.
13. A ball is thrown vertically upwards with a speed of 15m/s from a point 1m above the ground. Find the
speed with which it hits the floor. If it rebounds with a speed which is half the speed with which it hits
the floor, find its greatest height after the first bounce.
14. A metal ball is dropped from a height of 6.0 m onto soft ground. The ball hits the ground and penetrates a
distance of 8.5 cm. Calculate the deceleration of the ball as it enters the ground. You may assume that
the ball decelerates uniformly.