Question 8.5: Useful Physics for Safer Driving A car traveling at an initi......
Useful Physics for Safer Driving
A car traveling at an initial speed v slides a distance d to a halt after its brakes lock. If the car’s initial speed is instead 2 v at the moment the brakes lock, estimate the distance it slides.
Let us assume the force of kinetic friction between the car and the road surface is constant and the same for both speeds. According to Equation 8.14,
K_{f}=K_{i}-f_{k}d+\sum W_{\text{other forces }} (8.14)
the friction force multiplied by the distance d is equal to the initial kinetic energy of the car (because K_{f}=0 and there is no work done by other forces). If the speed is doubled, as it is in this example, the kinetic energy is quadrupled. For a given friction force, the distance traveled is four times as great when the initial speed is doubled, and so the estimated distance the car slides is 4 d.