Question

) with the box still on the truck, the truck attains its maximum velocity. as the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding?

Answer 1

When the truck starts decelerating a force starts acting on a box. In order for the box to start sliding force acting on it has to be bigger than a static force of friction.
If the trucks declaration is we have the following force acting on the box:

`F=ma`
This force has to be smaller than static friction force:

`F_f=mg\mu`
Where
`\mu` is static friction coefficient.
Now we can find an answer:

`ma\leq mg\mu\\ a\leq g\mu`