# Free body diagram with forces of friction

I think that this is a very interesting problem which is conceptually difficult.

You do not need to worry about the FBD for the truck. The box should be your main focus.

Diagram 1 is the FBD as long as the box does not slide relative to the truck.
With the aid of diagram 1 work out the maximum acceleration $a$ the box can have as a result of the static frictional force $\mu_sN_{bt}$ acting on it.
Hopefully this will lead you swiftly onto phase two of the problem and the FBD diagram 2.

Now this is where you might think that the kinetic friction direction is incorrect because it is actually going to make the box move faster as you might have heard the statement "friction opposes motion"? In this case the reason for the kinetic friction acting in the direction shown is that the kinetic frictional force is trying to reduce the relative velocity between the box and the truck. So it is relative motion that kinetic friction opposes and sometimes, as in this case, it has to make something go faster in order to try an achieve this.

Your conceptual problems are possibly not over yet as you now have the difficult task of having a truck accelerating to the right and a box accelerating to the right and you have to figure out how long it will take the box to move a given distance on the truck and fall off.

You might a good way of doing this is to draw, using the same axes, graphs of velocity against time for the truck and the box and remember that the area under a $v-t$ graph is the displacement (distance + direction).