A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10 m.If the coefficient of kinetic friction between the sled and the surface is 0.20,what was the initial speed of the sled?
A)9.8 m/s
B)6.3 m/s
C)3.6 m/s
D)7.2 m/s
E)8.9 m/s

Question

Quizplus · Accepted Answer

The work done by friction is equal to the change in kinetic energy. The force of friction $f_k = \mu_k N$, where $\mu_k = 0.20$ is the coefficient of kinetic friction and $N$ is the normal force, which equals the weight of the sled for a horizontal surface. The work done by friction is $f_k \times d$, where $d = 10$ m is the distance. The change in kinetic energy is $\Delta KE = \frac{1}{2}mv^2 - 0$, since the sled comes to rest. Setting the work done by friction equal to the change in kinetic energy and solving for $v$ gives the initial speed. Using the equation for work done by friction and the equation for kinetic energy, we find that the initial speed of the sled is approximately 6.3 m/s.

A Sled Having a Certain Initial Speed on a Horizontal