A box **(400 kg)** sits inside the trailer of a semitruck traveling at a **speed of 25 m/s **(~ 55 mph). Suddenly, a car in front of the truck stops in the road. The driver of the truck hits the brakes to bring the truck to a stop. Assume that the coefficient of **static friction µ _{s} = 0.7** between the box and the floor of the trailer. Assume g = 10 m/s

^{2}.

a) When the truck **slows down** while traveling left, what is the **direction** of the **friction** force on box 1 (right, left, none)?

b) When the truck is slowing down, what is the **maximum magnitude** of the static **friction** force on box 1 (to slow it down with the truck and not let it slide)?

N

c) When the truck is slowing down, what is the **maximum magnitude** of the truck’s **acceleration** such that box 1 does not slide?

m/s^{2}

d) What is the **minimum time** for the truck to stop such that box 1 does not slide? Use your maximum acceleration from the previous problem.

s

e) Given this minimum time, what is the **minimum distance** for the truck to stop without box 1 sliding?

m