Coal on conveyor belt

A conveyor belt with length $L=25\text{ m}$ moves at a constant velocity of $v$ to the left. Initially, a coal with mass $m$ was put on the midpoint of the conveyor belt, as shown. The coefficient of kinetic friction between the coal and the conveyor belt is $\mu = 0.1$ and the gravitational acceleration is $g=10\text{ m/s}^2.$

When the coal moves relatively to the conveyor belt, it will make a trace on the conveyor belt. Find the minimum velocity $v$ (in meters per second) of the conveyor belt such that the trace is not greater than $\frac{L}{2}.$

Bonus: Find the general formula for the minimum velocity $v$ in terms of $\mu, g,$ and $L.$