As soon as a traffic light turns green a car speeds up from rest to 50.0 mi/h with a constant acceleration of 9.90 mi/h.s. in the adjoining bike lane, a cyclist speeds up from rest to 20.0 mi/h with a constant acceleration of 13.5 mi/h.s. Each vehicle maintains a constant velocity after reaching its cruising speed.
(a) For how long is the bicycle ahead of the car?
(b) By what maximum distance does the bicycle lead the car?