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

1 answer

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