Answer to Question #239488 in Physics for rshiii

Question

13. The brakes of a 1000 kg automobile can exert a retarding force of 3000N. Find the distance the car will move before stropping if it is traveling at the rate of 24 m/s when the brakes are applied (96 m).

Answer 1

Given:

$m=1000\;\rm kg$

$F_f=3000\:\rm N$

$v_i=24\:\rm m/s$

The energy-work theorem says

$$\frac{mv_f^2}{2}-\frac{mv_i^2}{2}=W=-F_fd$$

Hence, the distance traveled by the car to rest

$$d=\frac{mv_i^2}{2F_f}=\frac{1000*24^2}{2*3000}=96\:\rm m$$