A Beautiful Problem

Classical Mechanics Level 2

A locomotive of mass $m$ starts moving so that its velocity varies according to the law $v=k \sqrt{s}$ , where $k$ is a constant and $s$ is the distance covered. Find the total work performed by all the forces which are acting on the locomotive during the first $t$ seconds, after the beginning of motion.

If $W=\large\frac { m{ k }^{ \alpha }{ t }^{ \beta } }{ \mu }$ , find $\alpha +\beta +\mu$ .