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# An object of mass 1 kg travelling at 5.0 m/s enters a region of ice where the coefficient of kinetic friction is .10. Find the distance the object travels before coming to rest.

$\begin{array}{1 1} 13\;m \\ 26\;m \\ 14\;m \\ 28\;m \end{array}$

According to the Work-Energy theorem, $W = \Delta KE$, where $W = - f_kd = -\mu_k N d = -\mu_k mgd$ and $\Delta KE = -\large\frac{1}{2}$$mv_i^2. \Rightarrow -\mu mgd =-\large\frac{1}{2}$$ mv_i^2$
$\Rightarrow d = \large\frac{1}{2\mu g }$${v_i^2} = \large\frac{1}{2 \times 0.1 \times 9.8}$$ 25 = 13\; m$
edited Aug 25, 2014