As soon as a traffic light turns green, a car speeds up from rest to 58.0 mi/h with constant acceleration 10.00 mi/h/s. in the adjoining bike lane, a cyclist speeds up from rest to 19.0 mi/h with constant acceleration 14.50 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?
(b) by what maximum distance does the bicycle lead the car?

Part a)

Part b)

Explanation:

Part a)

cruising velocity of bicycle = 19 mi/h

acceleration = 14.50 mi/h/s

For the motion of car

cruising velocity of car = 58 mi/h

acceleration = 10 mi/h/s

Both start from rest

Now we have

time taken by bicycle to reach its cruising speed is given as

Time taken by car to reach its cruising speed

now the distance moved by the car = distance moved by bicycle

till the time cycle moving in front of car

distance moved by the car =

distance moved by bicycle =

Part b)

Bicycle will lead the car till the speed of car and speed of bicycle is same

so we have

so the distance between them is given as