A man driving his car into 20.0 ft garage with a velocity of 20.0mi/h applies the brakes, producing a constant deceleration. Find the smallest deceleration necessary to avoid striking the back wall of the garage. And find how many seconds it takes for the car to come to rest

Answer 1

v = Vi + a t
v = 0 after 20 ft we hope
Vi = 20 * 5280ft/mi /3600s/h = 29.33 ft/s
so
a t = -29.33
a = -29.33/t

d = Vi t + (1/2) a t^2
20 = 29.33 t + .5 (-29.33/t)(t^2)
20 = .5 * 29.33 t
t = 1.36 seconds
a = - 21.6 ft/s^2