A pickup truck is carrying a toolbox, but the rear gate of the truck is missing,

Question

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is set moving. The coefficients of kinetic and static friction between the box and the bed of the truck are 0.260 and 0.550, respectively.

Starting from rest, what is the shortest time this truck could accelerate uniformly to 38.0 m/s ( 85.0 mph ) without causing the box to slide. (Hint: First use Newton’s second law to find the maximum acceleration that static friction can give the box, and then solve for the time required to reach 38.0 m/s .)

Explanation / Answer

Box will not move if frictional force on the block is larget than m*acceleration of truck

frictional force = mius*m*g

lets find maximum acceleratiuon possible:

mius*m*g = m*a

mius*g = a

a = 0.55*9.8 = 5.39 m/s^2

use:

vf= vi + a*t

38 = 0 + 5.39*t

t=7.05 s

Answer: 7.05 s

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