An object of mass m with a certain initial speed on a horizontal surface comes to rest after traveling a distance of 9.0 m. If the coefficient of kinetic friction between the object and the horizontal surface is 0.20, what is the initial speed of the object? Use g = 10 m/s².

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Quizplus · Accepted Answer

The work done by the force of kinetic friction is:$$W_f=F_fd=\mu_kmgd$$The change in kinetic energy of the object is:$$K_f-K_i=-\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$By the work-energy theorem, we have:$$W_f=K_f-K_i$$Substituting the expressions for $W_f$ and $K_f-K_i$, we get:$$\mu_kmgd=-\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$Since the object comes to rest, $v_f=0$, so we have:$$\mu_kmgd=-\frac{1}{2}mv_i^2$$Solving for $v_i$, we get:$$v_i=\sqrt{2\mu_kmgd}=\sqrt{2(0.20)(10	ext{ m/s}^2)(9.0	ext{ m})}=\boxed{6.0	ext{ m/s}}$$

An Object of Mass M with a Certain Initial Speed