Question

A 0.80 10^3 kg Toyota collides into the rear end of a 2.6 1^03 kg Cadillac stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 5.0 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.40, calculates the speed of the Toyota at impact. What is that speed?

Answer 1

m g down
mu m g friction force

F = m a
mu m g = m a

a = mu g = .4 (9.81) = 3.92 m/s^2

a = change in speed/time

change in speed = v
average speed during stop = v/2
distance = average speed * time
5 meters = v/2 t
so
t = 10/v

a = v /(10/v) = v^2/10
so
v^2/10 = 3.92
v^2 = 39.2
v = 6.26 m/s