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1. A car accelerates uniformly from rest to a speed of 90 km per hour in 10 seconds. How far, in metres, has the car travelled in this time?
2. A train starts from rest and accelerates uniformly to a speed of 30 m s-1 in 20 seconds. It travels at this speed for a further 1 minute. How far, in metres, has the train travelled in total?
3. A cyclist travels 1.3 km while accelerating uniformly from a speed of 15 km h-1 to 30 km h-1. Find the acceleration of the cyclist in m s-2.
4. A driver is travelling at 70 km h-1. The driver applies the brakes and decelerates at 5 m s-2. How much further, in metres, does the driver travel before coming to a stop?
5. A ball is dropped and takes 1.5 seconds to reach the ground. What is the speed of the ball, in m s-1, as it hits the ground?
6. A ball is thrown vertically upwards with an initial speed of 10 m s-1 from the ground. Find the maximum height of the ball.
7. A ball is thrown vertically upwards at a speed of 25 m s-1 at the same time as another ball is thrown vertically downwards from the same point at a speed of 25 m s-1. How far apart, in metres, are the balls after 2 seconds?
8. A train is brought to rest with uniform deceleration. It travels 30 m in the first 2 seconds and a further 30 m in the next 4 seconds. Find the total time, in seconds, the train takes to stop.
9. A man throws a coin vertically upwards with a speed of 2 m s-1. His hand is initially 1.2 m above the ground. Find the time taken for the coin to hit the ground.
10. A particle is projected vertically downwards from a great height and hits the ground with a speed of 28 m s-1. Find the time, in seconds, it took the particle to cover the last 15 metres of its motion.
11. A car travelling with constant acceleration $a$ m s-2 has an initial speed of 5 m s-1. In 20 seconds, it travels 500 metres. How long, in seconds, did it take the car to travel 300 metres?
12. A particle, $P$, is projected vertically upwards with speed 17.5 m s-1 from a point $A$, which is above horizontal ground. $P$ moves freely under gravity and hits the ground 5 seconds later with speed $V$ m s-1.
A second particle, $Q$, is thrown vertically upwards with speed $U$ m s-1 from $A$ and hits the ground with speed $\dfrac{6}{7}V$ m s-1. Find the exact value of $U$.
13. A car travels with constant acceleration $a$ m s-2 with initial speed 11 m s-1. In the time it takes the car to travel 28 m, the car accelerates to 17 m s-1. What is the total length of time, in seconds, the car takes to accelerate from 11 m s-2 to 29 m s-2?
14. A particle $P$ is released from rest from a point $h$ m above ground. One second later, a second particle $Q$ is thrown vertically downwards with speed 19.6 m s-1 from the same point $P$ was released. The particles reach the ground at the same time. Find $h$.
15. At time $t = 0$ s, two particles $A$ and $B$ are projected vertically upwards with speeds 13 and 3 m s-1 respectively. $A$ is projected from the ground while $B$ is projected from 20 m above the ground. At time $t = T$ seconds, both particles are at the same height above ground. Find $T$.
16. A runner passes through a checkpoint in a race with a speed of 3 m s-1 and finishes the race with a speed of 5 m s-1. A second runner passes through the same checkpoint 1 second later with a speed of 4 m s-1 and finishes the race with a speed of 8 m s-1. Both runners are accelerating constantly between the checkpoint and the finish, and they finish the race at the same time. Find the distance, in metres, between the checkpoint and the end of the race.
17. A particle, $P$, is projected vertically upwards from the ground with a speed of 30 m s-1. A second particle, $Q$, is projected vertically upwards from the top of a tower, of height 25 m, with a speed of 10 m s-1 at the same time. Find the height above the ground, in metres and correct to 3 significant figures, of the particles when they are at the same height.
18. A stone is thrown vertically upwards into the air at $u$ m s-1. A second stone is thrown vertically upwards into the air 2 seconds later at a speed of $0.5u$ m s-1. When the second stone reaches its maximum height, the two stones collide. Find the time taken, in seconds, between the first stone being thrown and the collision, correct to 3 significant figures.