## Question

A car travelling at a constant speed of 30 ms_{-1} passes a police car, which is at rest.

The police officer accelerates at a constant rate of 3.0 ms_{-2} and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the car moves past the police car.

What is the time required for the police officer to catch up with the car?

## Answer

We assume that the police car catches up with the car at time t_{1}.

The following formula for displacement can be obtained:

When the police car catches up with the car, both have travelled the same displacement.

The police car requires 20 s to catch up with the car.