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)690 N
B)550 N
C)410 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 (KE) of the car is $ \frac{1}{2}mv^2 $, where $ m = 1100 \, \text{kg} $ is the mass of the car and $ v = 27 \, \text{m/s} $ is its initial velocity. The final kinetic energy is 0 (since the car comes to a stop). Therefore, the work done by the braking force is equal to the initial kinetic energy:$$ \text{Work} = \Delta KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 1100 \times 27^2 $$$$ \text{Work} = \frac{1}{2} \times 1100 \times 729 = 400950 \, \text{J} $$The work done is also equal to the force times the distance over which it acts (Work = Force × Distance), so:$$ 400950 = F \times 578 $$Solving for $ F $:$$ F = \frac{400950}{578} \approx 693.6 \, \text{N} $$Rounding to the nearest whole number gives a force of approximately 690 N.

A Car of Mass 1100 Kg That Is Traveling at 27