A body is moving down a long inclined plane of angle of inclination $\mathrm{\theta }$. The coefficient of friction between the body and the plane varies as $\mathrm{\mu }$ = 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

• A

  $\mathrm{x}=2\tan \mathrm{\theta }$

• B

  $\mathrm{x}=\frac{2}{\tan \mathrm{\theta }}$

• C

  $\mathrm{x}=\sqrt{2}\cot \mathrm{\theta }$

• D

  $\mathrm{x}=\frac{\sqrt{2}}{\cot \mathrm{\theta }}$