An 1100-kg car traveling at 27.0 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) 690 N
B) 550 N
C) 410 N
D) 340 N

Question

Quizplus · Accepted Answer

The magnitude of the average braking force can be found 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 (KE) of the car is $ \frac{1}{2}mv^2 $, where $ m = 1100 \, \text{kg} $ is the mass of the car and $ v = 27.0 \, \text{m/s} $ is its initial velocity. The final kinetic energy is 0 (since the car comes to a stop). Thus, the change in kinetic energy is $ \Delta KE = 0 - \frac{1}{2} \cdot 1100 \cdot 27.0^2 $.The work done by the braking force is also given by $ W = F \cdot d $, where $ F $ is the average braking force and $ d = 578 \, \text{m} $ is the distance over which the force is applied. Setting the work equal to the change in kinetic energy gives $ F \cdot 578 = -\frac{1}{2} \cdot 1100 \cdot 27.0^2 $.Solving for $ F $ gives $ F = -\frac{\frac{1}{2} \cdot 1100 \cdot 27.0^2}{578} \approx -690 \, \text{N} $. The negative sign indicates that the force is in the opposite direction of the car's initial motion, which is expected for a braking force. The magnitude of this force is 690 N.

An 1100-Kg Car Traveling at 27