An automobile approaches a barrier at a speed of 20 m/s along a level road. The driver locks the brakes at a distance of 50 m from the barrier. What minimum coefficient of kinetic friction is required to stop the automobile before it hits the barrier?
A)0.4
B)0.5
C)0.6
D)0.7
E)0.8

Question

Quizplus · Accepted Answer

The minimum coefficient of kinetic friction required to stop the automobile before it hits the barrier is 0.4. This is because the force of kinetic friction is equal to the coefficient of kinetic friction times the normal force. The normal force is equal to the weight of the automobile, which is equal to its mass times the acceleration due to gravity. The force of kinetic friction is equal to the mass of the automobile times its acceleration. Therefore, the coefficient of kinetic friction is equal to the acceleration of the automobile divided by the acceleration due to gravity. The acceleration of the automobile is equal to the change in velocity divided by the time. The change in velocity is equal to the final velocity minus the initial velocity. The final velocity is zero, and the initial velocity is 20 m/s. The time is equal to the distance traveled divided by the speed. The distance traveled is 50 m, and the speed is 20 m/s. Therefore, the time is 2.5 s. Therefore, the acceleration of the automobile is -8 m/s^2. The acceleration due to gravity is 9.8 m/s^2. Therefore, the coefficient of kinetic friction is -8 m/s^2 / 9.8 m/s^2 = 0.4.

An Automobile Approaches a Barrier at a Speed of 20