$u=u$

For mass 'm', N=mg

$f=\mu m g$

$a=\frac{\mu m g}{m}=\mu g$

Here $a=$ retardation by friction $=-\mu g=-c g x$ Because

$a=v \frac{d v}{d x}=-c g x$

$\int_{u}^{o} v d v=-c g \int_{0}^{x} x d x$

$\Rightarrow\left[\frac{v^{2}}{2}\right]_{u}^{o}=-c g\left(\frac{x^{2}}{2}\right)_{o}^{x}$

$\frac{-u^{2}}{2}=-\frac{c g x^{2}}{2}$

$\Rightarrow x=\frac{u}{\sqrt{c g}}$