4.1.9

# Bouncing Ball Example

Test yourself

## Motion of a Bouncing Ball

To illustrate the concepts of motion in a straight line, let's consider a ball bouncing up and down. The ball starts at rest at 10 metres.

### Displacement-time graph

• The ball starts (at time t = 0) at a height of 10 metres.
• The ball falls towards the ground.
• After the ball has hit the ground, it bounces back up.
• The same process repeats with the ball starting from a little lower each time.

### Velocity-time graph

• To begin with (at t = 0), the ball is at rest (v = 0).
• The ball is then released and falls towards the ground.
• By convention, upwards is usually positive, so falling towards the ground means a negative velocity.
• The longer the ball falls, the quicker it gets.
• The ball hits the ground and instantaneously its velocity is reversed, it is now travelling upwards.

### Velocity-time graph 2

• The further the ball travels upwards, the slower it gets - its velocity decreases but stays positive.
• When the velocity decreases to zero, the ball is at the top of its bounce, instantaneously at rest.
• The ball then falls and its velocity becomes increasingly negative.
• The cycle is repeated for every bounce.

### Acceleration-time graph

• The acceleration of the ball is always the same: the acceleration due to gravity.
• The acceleration due to gravity is -9.81 m/s2.
• It is negative because it is pulling the ball downwards.