speed - distance catching up

*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!