What is the minimum stopping distance if the load is not to slide forward in the cab?

Question

An object of mass 6000 kg rests on the flatbed of a truck. It is held in place by metal brackets that can exert a maximum horizontal force of 9000 N. When the truck is traveling 15 m/s, what is the minimum stopping distance if the load is not to slide forward in the cab?

Answer 1

Let:

S = the minimum stopping distance

V = the velocity

a = the acceleration

F = force due to acceleration

F = ma = 6000a = 9000

a = 9000/6000 = 1.5 m/sec^2

S = V^2/(2a) = 15^2/(2 x 1.5) = 225/3 = 75 m

Answer 2

Let:

a be the acceleration,

s be the stopping distance.

9000 >= 6000a

a <= 1.5 m/s^2 ... (1)

0 = 15^2 - 2as

a = 225 / (2s)

Substituting for a in (1):

225 / (2s) <= 1.5 m/s^2

s >= 225 / 3

s >= 75 m.