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# Time required to stop a truck with specified retardation

I am working on a losing cargo problem. I have a box of mass 12.7kg that rests on the flat floor of my truck. My coefficents of friction between the box and floor are u8 =0.180 and uk=0.160. TMy truck stops at a stop sign and then starts to move with an acceleration of 2.15m/s2 . (That s squared.) So if the box is a distance 1.81m from the rear of the truck when I start it, how much time will elapse before the box falls of my truck?

Assume the free fall acceleration to be g=9.80m/s2.(That's s squared)

Also how far does my truck travel in this amount of time . Assume the free fall acceleration to be g=9.80 /s2 (That's s squared.)

Thanks for your help!

#### Solution Preview

For the object to move, it must at first overcome the force of static friction. So first we will check whether the mass will get that amount of force when the truck accelerates.

Force of static friction, F_s = mu * mg = 0.18*12.7*9.8 = 22.4 N

Now, the truck starts to move with an acceleration of 2.15m/s^2, which exerts a force of m*a on ...

#### Solution Summary

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