# A Beautiful Problem

**Classical Mechanics**Level 3

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 \(\alpha +\beta +\mu \).