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 with the distance travelled as $\mu =0.5x$. Where x is the distance moved down the plane. The body will have maximum velocity, when it has travelled a distance x, given by: 

Net force acting on the body along the incline is $F=mg\sin \theta -\mu \mathrm{mgcos}\theta =mg(\sin \theta -0.5x\cos \theta )$

The value net force reduces to zero when 

$$\begin{gathered} \sin \theta -0.5x\cos \theta =0 \\ \mathrm{x}=2\tan \theta \end{gathered}$$

Till this point, velocity increases. Beyond this point, the direction of F reverses and velocity starts decreasing. Hence, this is the position where the velocity is maximum.