Using the law of conservation of energy.

Explanation

Here the work of the force of friction T is equal to the decrease in kinetic energy .In the reference frame of the platform
`Tl = K_(0) " or " mumgl=(mv_0^2)/2` , whence `l=(v_0^2)/(2mug)`
The braking time is
`tau=l/(v_(av))=(2l)/(v_0)=(v_0)/(2mug)`