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)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 initial speed of the object 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 of the object, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $d$ is the distance (10 m). The change in kinetic energy is $\Delta KE = \frac{1}{2} m v^2 - 0$, since the object comes to rest. Setting the work done by friction equal to the change in kinetic energy and solving for $v$ gives $v = \sqrt{2 \cdot \mu_k \cdot g \cdot d}$. Substituting $\mu_k = 0.20$, $g = 9.8 \, \text{m/s}^2$, and $d = 10 \, \text{m}$, we find $v \approx 6.3 \, \text{m/s}$.

A Sled Having a Certain Initial Speed on a Horizontal