# Preventing a box from sliding.

1. A person driving a truck has a box in the back. They are driving at a constant speed (v_0) when they notice a red light and have to stop. What is the maximum acceleration the truck can have without causing the box to slide forward? (Answer must be given in terms of variables, as no values are given)

2. Sum of forces in the x direction=m*a, f_s=$$\mu$$*n= $$\mu$$*mg.

3. The thing that confuses me most is the acceleration. I assume the acceleration is negative because the truck is slowing down. I don't understand what force is acting on the box to slide it forward (I know friction is pushing it back), or how to measure that force. I assume f_s has to equal that force so the box doesn't move, but if it does, the sum of forces = 0, and thus m*a=0, thus a=0. But a can't be zero! So how do I solve for a?