# A body is moving down a long inclined plane of angle of inclination $\theta$ . The coefficient of friction between the body and the plane varies as $\mu =0.5 \;x$ Where x is the distance moved down the plane . The body will have the maximum velocity when it has travelled a distance x given by
$\begin{array}{1 1}x=2 \;\tan \;\theta \\ x= \large\frac{2}{\tan \theta}\\x= \sqrt 2 \cot \theta \\x= \large\frac{\sqrt 2}{\cot \theta}\end{array}$