friction, physics?

Question

A box of mass m rests on the flat floor of a truck. The coefficients of friction between the box and floor are µ_s and µ_k. The truck stops at a stop sign and then starts to move with an acceleration of a.

If the box is a distance x from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck?
Take the free fall acceleration to be g .

How far does the truck travel in this time?
Take the free fall acceleration to be g.

Answer 1

a must be greater than mu_s g

t = sqrt (x/(a - mu_k g))

distance traveled by truck = 1/2 a t^2 = ax/(2*(a - mu_k g))