## Physics: Principles with Applications (7th Edition)

For a constant stopping force, the stopping distance isn’t proportional to the speed. In fact, the stopping distance is proportional to the initial kinetic energy, because the work done by the stopping force brings the car to rest. The kinetic energy is proportional to the square of the speed, i.e., $KE = \frac{1}{2} mv^{2}$. Doubling the car’s initial speed will quadruple the initial kinetic energy and also quadruple the stopping distance.