A small block starts sliding down an inclined plane subtending an angle `theta` with the horizontal . The coefficient of friction between the block and plane depends on the distance covered from rest along the plane as `mu = mu_(0)x` where `mu_(0)` is a constant . Find (a) the distance covered by the block down the plane till it stops sliding and (b) its maximum velocity during this journey .

Answer

`d + ( sin theta + sqrt( sin^(2) theta + d mu_(0) sin 2 theta))/( mu _(0) co stheta )`