Question

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 .)

Answer 1

`t = 5.95 s`

Step-by-step explanation:

As we know that the coefficient of static friction between box and the truck is given as

`\mu_s = 0.65`

so the maximum static friction force on the box so that it will not slide on the truck is given as

`F_f = \m_s mg`

so maximum possible acceleration of the box is given as

`a = \mu_s g`

`a = 0.65 (9.81)`

`a = 6.38 m/s^2`

now time to reach the given speed is

`v = v_i + at`

`38 = 0 + 6.38 t`

`t = 5.95 s`