Thus the velocity of the speeder is 27.0 m/s and i'm assuming it remains at that speed.

The initial velocity of the police car then is u = 0m/s and its acceleration is 2.94m/s^2 and this does not change.

You should be immediately looking to use the SUVAT equations (constant acceleration) and probably want to set up this problem so that both cars are at the exact same point in space when we can consider the police car to have caught up/overtaken the speeder... i.e. they've both travelled the same distance, s.