HARD
AS and A Level
IMPORTANT
Earn 100

A car accelerates from rest to a speed v m s-1 at a constant acceleration. It then immediately decelerates at a constant deceleration until coming back to rest t s after starting the motion. Suppose instead the car spends a time T s at speed v m s-1 but still returns to rest after a total of t s after starting the motion. Show that the distance travelled is independent of the values of the acceleration and deceleration.

Important Questions on Velocity and Acceleration

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 1
An ice hockey puck slides along a rink at a constant speed of 10 m s-1. It strikes the boards at the edge of the rink 20 m away and slides back along the rink at 8 m s-1 until going into the goal 40 m from the board. Sketch a velocity-time graph and a displacement-time graph for the motion, measuring displacement from the starting point in the original direction of motion.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 2

A bowling ball rolls down an alley with initial speed 8 m s-1 and decelerates at a constant rate of 0.8 m s-2. After 2.5 s it strikes a pin and instantly slows down to 2 m s-1. It continues to decelerate at the same constant rate until coming to rest.

Sketch a velocity-time graph and a displacement-time graph for the motion.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 3
In a game of blind cricket, a ball is rolled towards a player with a bat 20 m away, who tries to hit the ball. On one occasion, the ball is rolled towards the batsman at a constant speed of 4 m s-1. The batsman hits the ball back directly where it came from with initial speed 6 m s-1 and decelerating at a constant rate of 0.5 m s-2. Sketch a velocity-time graph and a displacement-time graph for the motion, taking the original starting point as the origin and the original direction of motion as positive.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 4
A ball is dropped from rest 20 m above the ground. It accelerates towards the ground at a constant rate of 10 m s-2. It bounces on the ground and leaves with a speed that is half the speed it struck the ground original. The ball is then caught when it reaches the highest point of its bounce. Sketch a velocity-time graph and a displacement-time graph for the motion, measuring displacement above the ground.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 5
A ball is thrown towards a wall, which is 5 m away, at 2.25 m s-1. It slows down at a constant rate of 0.2 m s-2 until it strikes the wall. It bounces back at 80% of the speed it struck the wall originally. It again slows down at a constant rate of 0.2 m s-2 until coming to rest. Sketch a velocity-time graph and a displacement-time graph for the motion, measuring displacement from the wall, taking the direction away from the wall as positive.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 6

A billiard ball is on the centre spot of a 6 m long table and is struck towards one of the cushions with initial speed 3.1 m s-1. It slows on the table at 0.2 m s-2. When it bounces of the cushion its speed reduces to 70% of the speed with which it struck the cushion. The ball is left until it comes to rest.

Sketch the velocity-time and displacement-time graphs for the ball, taking the centre of the table as the origin for displacement and the original direction of motion as positive.

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 6

A billiard ball is on the centre spot of a 6 m long table and is struck towards one of the cushions with initial speed 3.1 m s-1. It slows on the table at 0.2 m s-2. When it bounces of the cushion its speed reduces to 70% of the speed with which it struck the cushion. The ball is left until it comes to rest.

What assumptions have been made in your answer?

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1F>Q 7
A ball is released from rest 20 m above the ground and accelerates under gravity at 10 m s-2. When it bounces its speed halves. If bounce n occurs at time tn the speed after the bounce is vn. Show that vn=15-2.5tn and deduce that, despite infinitely many bounces, the ball stops bouncing after 6 s.