By what percent does the braking distance of a car increase when the speed of the car increases by 13.9 percent?

(Note: Braking distance is the distance a car travels from the point when the brakes are applied to when the car comes to a complete stop.)

Question

High School

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Answer :

nobomika97 nobomika97 · Answer 1 · 2025-02-27T04:59:30-05:00

the braking distance increases by approximately 29.721 percent when the speed of the car increases by 13.9 percent.

Given: Speed of the car increases by 13.9 percent

Let v be the original velocity of the car.

When the speed increases by 13.9 percent, the new velocity becomes 1.139v.

Kinetic energy (KE) is directly proportional to the square of velocity.

Therefore, the kinetic energy of the car increases by [tex](1.139)^2[/tex] times or approximately 1.29721 times.

Braking distance is directly proportional to kinetic energy.

Hence, the braking distance increases by the same factor of 1.29721 times or approximately 29.721 percent.

So, the braking distance increases by approximately 29.721 percent when the speed of the car increases by 13.9 percent.