Acar starts from rest and accelerates at a constant rate until it reaches 70 mi/hr in a distance of 220 ft, at which time the clutch is disengaged. the car then slows down to a velocity of 40 mi/hr in an additional distance of 480 ft with a deceleration which is proportional to its velocity. find the time t for the car to travel the 700 ft.

Explanation:

During deceleration we know that the deceleration is proportional to the velocity

so we have

here we know that

so we have

now integrate both sides

Also we know that

so from above equation

initially it starts from rest and uniformly accelerate to maximum speed of 70 mph and covers a distance of 220 ft

so we have

d = 220 ft = 67 m = 0.042 miles[/tex]

now we know that

so total time of motion is given as