Will the Box Move on a Braking Truck? Mathematical Justification Required

[tonya]

Homework Statement

A box with a mass of 5 kg sits in the middle of the bed of a pickup truck moving with a speed of 90 km/h. The maximum force of friction between the box and the truck is 15N. If the truck were braked uniformly to a stop in 125 m, would the box move? Justify your answer mathematically.

Homework Equations

vf2= vo2 + 2ax?

The Attempt at a Solution

a= (vf2 - vo2) / 2x
a= (0-9) / 2(125)
a= -0.36
yes is would
am i even close?

 

[mgb_phys]

Almost correct .

Calculate the acceleration of the truck - make sure you use consistent units.
Then draw a diagram of the forces acting horizontally on the box, remember f=ma

 

[tonya]

right so, 90 km/h is 25m/s. therefore acceleration [of truck] is equal to -0.1m/s2

 

[mgb_phys]

Think you have a calculator error there
a = v²/ 2s = 25² / 2*125 ms^-2