Box Mass and Friction: Calculating Time Before Fall

[trajan22]

A box of mass 12.5 kg rests on the flat floor of a truck. The coefficients of friction between the box and floor are mu_s = 0.190 and mu_k = 0.150 . The truck stops at a stop sign and then starts to move with an acceleration of 2.19 m/s^{2}.
If the box is a distance 1.79 m from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck?

my only question with this problem is how the static friction and kinetic frictional forces are related when calculating the final force...i know how to get each of these frictional forces just now how to put them together since kfriction acts over the entire movement while sfriction only acts for on instant

 

[Doc Al]

Assume that truck begins its acceleration instantly. If the acceleration is enough to make the box slip along the floor of the truck, then you only need to consider kinetic friction when finding the forces on the box.

 

[trajan22]

oh ok well that makes this problem infinitely easier than i thought