An object of mass m with a certain initial speed on a horizontal surface comes to rest after traveling a distance of 10 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:$$W_f = -f_k d = -\mu_k mgd$$The change in kinetic energy of the object is:$$\Delta K = K_f - K_i = 0 - \frac{1}{2}mv_i^2$$By the work-energy theorem, we have:$$W_f = \Delta K$$$$-\mu_k mgd = -\frac{1}{2}mv_i^2$$$$v_i = \sqrt{2\mu_k gd} = \sqrt{2(0.20)(10 	ext{ m/s}^2)(10 	ext{ m})}$$$$v_i = 6.3 	ext{ m/s}$$

An Object of Mass M with a Certain Initial Speed