Answer to Question #145560 in Physics for jesse

Question

. A bike and a rider, with a combined mass of 82.0 kg, travel at +4.2 m/s. A constant force of -
140 N is applied by the brakes in stopping the bike. What braking distance is needed?

Answer 1

We can find the braking distance from the Work-Kinetic Energy Theorem (the change in kinetic energy is equal to the work done by the friction force in stopping the bike):

$$KE_f-KE_i=W,$$ $$KE_f-KE_i=-F_{fr}s,$$ $$\dfrac{1}{2}mv_f^2-\dfrac{1}{2}mv_i^2=-F_{fr}s,$$ $$0-\dfrac{1}{2}mv_i^2=-F_{fr}s,$$ $$s=\dfrac{mv_i^2}{2F_{fr}},$$ $$s=\dfrac{82.0\ kg\cdot (4.2\ \dfrac{m}{s})^2}{2\cdot 140\ N}=5.16\ m.$$

Answer:

$s=5.16\ m.$