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 object and the surface is 0.20, what was the initial
Speed of the object?
A) 6.3 m/s
B) 8.9 m/s
C) 3.6 m/s
D) 7.2 m/s
E) 9.8 m/s

Question

Quizplus · Accepted Answer

The initial speed can be found using the work-energy principle. The work done by friction is equal to the change in kinetic energy. The work done by friction is $W = f_k \cdot d = \mu_k \cdot m \cdot g \cdot d$, where $\mu_k$ is the coefficient of kinetic friction, $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $d$ is the distance (10 m). The change in kinetic energy is $\Delta KE = \frac{1}{2} m v^2 - 0$, since the sled comes to rest. Setting the work done by friction equal to the change in kinetic energy and solving for $v$ gives $v = \sqrt{2 \cdot \mu_k \cdot g \cdot d}$. Plugging in $\mu_k = 0.20$, $g = 9.8 m/s^2$, and $d = 10 m$, we find $v \approx 6.3 m/s$.

A Sled Having a Certain Initial Speed on a Horizontal