A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m. What is the magnitude of the average braking force acting on the car?
A) 410 N
B) 690 N
C) 550 N
D) 340 N

Question

Quizplus · Accepted Answer

The magnitude of the average braking force can be calculated using the work-energy principle. The work done by the braking force is equal to the change in kinetic energy of the car. The initial kinetic energy is $ \frac{1}{2}mv^2 $, where $ m = 1100 \, \text{kg} $ and $ v = 27 \, \text{m/s} $. The final kinetic energy is 0 (since the car stops). Therefore, the work done by the braking force is $ -\frac{1}{2} \times 1100 \times 27^2 $. The work done is also equal to the force times the distance over which it acts, $ F \times d $, where $ d = 578 \, \text{m} $. Setting these equal and solving for $ F $ gives $ F = -\frac{1}{2} \times 1100 \times 27^2 / 578 $, which calculates to approximately $ 690 \, \text{N} $. The negative sign indicates the force is in the opposite direction of motion, but we are asked for the magnitude, so the answer is 690 N.

A Car of Mass 1100 Kg That Is Traveling at 27