A level Maths help

The car starts from rest at a fixed point A on the road and moves with constant acceleration for 30 seconds, reaching a speed of 15ms^(-1). This speed is then maintained. When the car has been moving for 15 seconds a motorbike starts from rest at A and moves along the same road in the same direction as the car. The motorbike accelerates at 1.5ms^(-2) so that it catches up with the car when the car has been moving for T seconds. Find the speed of the motorbike at the instant it catches up with the car. - So far I have done suvat and worked out that the car travelled 450m before the motorbike set off. However I cant use suvat or simultaneous equations to find T and I know that when they meet T and S for the car and motorbike will be the same. Do I need to differentiate or something?