A smooth block is released at rest on a $45^\circ$ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
(1) $\mu_\mathrm{k} = 1 - \frac{1}{\mathrm{n}^2}$
(2) $\mu_\mathrm{k} = \sqrt{1 - \frac{1}{\mathrm{n}^2}}$
(3) $\mu_s = 1 - \frac{1}{n^2}$
(4) $\mu_s = \sqrt{1 - \frac{1}{n^2}}$

A body starts from rest on a long inclined plane of slope $45^{\circ}$. The coefficient of friction between the body and the plane varies as $\mu = 0.3x$, where $x$ is distance travelled down the plane. The body will have maximum speed (for $g = 10\mathrm{~m/s^2}$) when $x =$
(1) 9.8 m
(2) 27 m
(3) 12 m
(4) 3.33 m