## College Physics (4th Edition)

The rate of deceleration comes from the force of kinetic friction exerted on the car. Note that the rate of deceleration is the same in both cases. Let $a$ be the magnitude of the deceleration. Since the car is slowing down, we can let the acceleration be $-a$. We can find an expression for the displacement when the car is moving with an initial velocity of $v_0$: $v_f^2 = v_0^2+2(-a)d$ $d = \frac{v_f^2 - v_0^2}{(2)(-a)}$ $d = \frac{0 - v_0^2}{-2a}$ $d = \frac{v_0^2}{2a}$ We can find the displacement $d_2$ when the initial velocity is $2v_0$: $d_2 = \frac{(2v_0)^2}{2a}$ $d_2 = 4\times \frac{v_0^2}{2a}$ $d_2 = 4d$ $d_2 = (4)(50~ft)$ $d_2 = 200~ft$ With an initial velocity of 60 mi/h, the car would skid 200 feet.