A speeding motorbike travels past a stationary police car. The police car starts accelerating immediately, and keeps accelerating until it has passed the bike.

DATA: motorbike speed: ; police car acceleration:

How far does the police car travel before it overtakes the motorbike?

I tried working this out using the following method, but it is wrong. How come?

My Solution

Let the distance travelled by the motorbike be and the distance travelled by the police car be . Let be time in seconds.

The distance travelled by the motorbike is given by

The distance travelled by the police car can be expressed by

When ,

Solving gives

Thankyou!