A car is moving across a level highway with a speed of 31.3 m/s. The brakes are applied and the wheels become locked as the 1290-kg car skids to a stop. The braking distance is 130 meters.

Question

What is the initial kinetic energy of the car? 

What is the final final energy of the car?  

How much work was done by the brakes to stop the car?

Determine the magnitude (enter your answer as a positive answer) of the constant braking force acting upon the car.  

Answer 1

Hi Charlotte,

The initial kinetic energy (KE) of the car:

KE_initial = 1/2 (mv²)

The final kinetic energy of the car is zero because the car comes to a complete stop at the end of this scenario. You may then wonder, "where did that initial energy go? isn't energy supposed to be conserved?" The energy didn't vanish, it was just transferred as heat during the braking process (the brake pads, tires, and the road that the car is skidding on will heat up - try "skidding" your finger across a carpet and you will feel this heat!). But the kinetic energy of the car has gone to zero.

KE_final = 0

So this means that the change in kinetic energy of the car is:

ΔKE = KE_final - KE_initial = 0 - 1/2 (mv²) = -1/2 (mv²)

Now, we also know that Work is equal to the change in energy. If there is work being done on an object, then there will be a change in that objects energy. In this case where the brakes are acting, we can then say.

W_{done by brakes} = ΔKE = -1/2 (mv²)

Then, to find the magnitude of the braking force, we can also remember that Work can also be described in the following definition:

W_{done by brakes} = F_brakes * Δx

where Δx is the stopping distance (the distance through which the braking force was applied)

So to get the magnitude of F_brakes, we can say

[F_brakes] = [W_{done by brakes} / Δx ]= (1/2 (mv²)) / Δx