As soon as a traffic light turns green, a car speeds up from rest to 54.0 mi/h with constant acceleration 8.00 mi/h/s. In the adjoining bike lane, a cyclist speeds up from rest to 27.0 mi/h with constant acceleration 12.00 mi/h/s. Each vehicle maintains constant velocity after reaching its cruising speed.

(a) For what time interval is the bicycle ahead of the car? (in seconds)

(b) By what maximum distance does the bicycle lead the car? (in feet)

Question

As soon as a traffic light turns green, a car speeds up from rest to 54.0 mi/h with constant acceleration 8.00 mi/h/s. In the adjoining bike lane, a cyclist speeds up from rest to 27.0 mi/h with constant acceleration 12.00 mi/h/s. Each vehicle maintains constant velocity after reaching its cruising speed.
 
 (a) For what time interval is the bicycle ahead of the car? (in seconds)

(b) By what maximum distance does the bicycle lead the car? (in feet)

anonymous · Answer

v1 = a1 t  = ( 8 mph/s) t  until  v1 = 54 mph at t1=?

v2 = a2 t = (12 mph/s) t   until = 27 mph at t2=?

probably best to graph these two.

For the distances, 
s1 = (1/2) a1 t^2 until  t1 plus an additional v1 (t-t1) thereafter 

s2 = (1/2) a2 t^2 until t2 plus an additional v2 (t - t2) thereafter.

Also best plotted?