Initially, a blue automobile has twice the kinetic energy that a red automobile has. Both are braked to a stop; both have the same amount of braking force. The red auto will stop in ____________________ as the blue auto.
A) half the distance
B) the same distance
C) twice the distance
D) four times the distance
E) one fourth the distance

Question

Quizplus · Accepted Answer

Since kinetic energy is directly proportional to the square of the velocity and the work done to stop the car (which is equal to the kinetic energy due to the work-energy principle) is the same for both cars, the distance covered during braking (work done against friction) is directly proportional to the kinetic energy. If the blue car has twice the kinetic energy, it will require twice the work to stop, implying it will stop in twice the distance. Thus, the red car will stop in half the distance compared to the blue car.

Initially, a Blue Automobile Has Twice the Kinetic Energy That