Block on a Conveyor Belt

A conveyor belt having a length \(l\) and carrying a block of mass \(m\)
moves at a velocity \(v\). Determine the distance covered by the block before it stops.

The initial velocity of the block relative to the ground is determined from the conditions $$ v_0=at$$ $$ l=v_0t-at^2/2$$
Now, acceleration of the block due to friction $$ a=\mu g$$
Hence, $$ v_0=\sqrt{2\mu gl}$$
The time of the motion of the block along the conveyor belt $$ t=\sqrt{\frac{2l}{\mu g}}$$
The distance covered by the block before it stops $$ s=l+vt=l+v\sqrt{\frac{2l}{\mu g}}$$

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