A billiard ball is on the centre spot of a $6 \mathrm{m}$ long table and is struck towards one of the cushions with initial speed $3.1 \mathrm{m}{ \mathrm{s}}^{-1}.$ It slows on the table at $0.2 \mathrm{m}{ \mathrm{s}}^{-2}.$ 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?

A man and his young son play a game. The man rolls a ball along the ground. His son runs after the ball to fetch it.

The ball starts rolling at $10 \mathrm{m}{ \mathrm{s}}^{-1}$ but decelerates at a constant rate of $2 \mathrm{m}{ \mathrm{s}}^{-2}.$ Find the distance covered when it comes to rest.

A man and his young son play a game. The man rolls a ball along the ground. His son runs after the ball to fetch it.

Once the ball has stopped, the boy runs to fetch it. He starts from rest beside his father and accelerates at a constant rate of $2 \mathrm{m}{ \mathrm{s}}^{-2}$ for $3 \mathrm{s}$ before maintaining a constant speed. Find the time taken to reach the ball.

A car is travelling at $15 \mathrm{m}{ \mathrm{s}}^{-1}$ when the speed limit increases and the car accelerates at a constant rate of $3 \mathrm{m}{ \mathrm{s}}^{-2}$ until reaching a top speed of $30 \mathrm{m}{ \mathrm{s}}^{-1}.$

Find the distance covered until reaching top speed.

A car is travelling at $15 \mathrm{m}{ \mathrm{s}}^{-1}$ when the speed limit increases and the car accelerates at a constant rate of $3 \mathrm{m}{ \mathrm{s}}^{-2}$ until reaching a top speed of $30 \mathrm{m}{ \mathrm{s}}^{-1}.$

Once the car is at top speed, there is a set of traffic lights $600 \mathrm{m}$ away. The car maintains $30 \mathrm{m}{ \mathrm{s}}^{-1}$ until it starts to decelerate at a constant rate of $5 \mathrm{m}{ \mathrm{s}}^{-2}$ to come to rest at the lights. Find the time taken from reaching top speed until it comes to rest at the traffic lights.

In a race, the lead runner is $60 \mathrm{m}$ ahead of the chaser with $200 \mathrm{m}$ to go and is running at $4 \mathrm{m}{ \mathrm{s}}^{-1}.$ The chaser is running at $5 \mathrm{m}{ \mathrm{s}}^{-1}.$

Find the minimum constant acceleration required by the chaser to catch the lead runner.

In a race, the lead runner is $60 \mathrm{m}$ ahead of the chaser with $200 \mathrm{m}$ to go and is running at $4 \mathrm{m}{ \mathrm{s}}^{-1}.$ The chaser is running at $5 \mathrm{m}{ \mathrm{s}}^{-1}.$

If the lead runner is actually accelerating at a constant rate of $0.05 \mathrm{m}{ \mathrm{s}}^{-2},$ find the minimum constant acceleration required by the chaser to catch the lead runner.