Newton's second law: 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

To find the magnitude of the average braking force, we can use 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_initial) of the car is given by $ \frac{1}{2}mv^2 $, where $ m = 1100 $ kg is the mass of the car and $ v = 27.0 $ m/s is its initial velocity. The final kinetic energy (KE_final) is 0 because the car comes to a stop. Therefore, the change in kinetic energy ($ \Delta KE $) is $ \frac{1}{2} \times 1100 \times 27.0^2 $. The work done by the braking force is also equal to the force times the distance over which it acts ($ F \times d $), where $ d = 578 $ m is the distance over which the car comes to a stop. Setting the work equal to the change in kinetic energy gives $ F \times 578 = \frac{1}{2} \times 1100 \times 27.0^2 $. Solving for $ F $ gives the magnitude of the average braking force. Plugging in the numbers, $ F = \frac{1}{2} \times 1100 \times 27.0^2 / 578 $ gives approximately $ 690 $ N.

Newton's Second Law: an 1100-Kg Car Traveling at 27