Question

A pickup truck is moving at 20 m/s when suddenly the breaks are applied, and the truck comes to a stop in 5s. A toolbox of mass M rests on the bed of the truck 1m from the cab. if the coefficient of kinetic friction between the toolbox and the bed of the truck is 0.2, how much time passes before the toolbox strikes the cab?

Answer 1

here,

the initial speed of truck , u = 20 m/s

time taken to stop , t = 5 s

let the acceleration of truck be a

using first equation of motion

0 = u + a * t

0 = 20 + a * 5

solving for a

a = - 4 m/s^2

coefficient of friction , uk = 0.2

the acceleration of toolbox , a' = a + uk * g

a' = -4 + 0.2 * 9.81 m/s^2

a' = - 2.038 m/s^2

let the time taken before the toolbox strikes the cab be t'

s = 0 + 0.5 * a' * t'^2

- 1 = 0 + 0.5 * (- 2.038) * t'^2

solving for t'

t' = 0.99 s

the time taken before the toolbox strikes the cab is 0.99 s