# 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 $$\alpha +\beta +\mu$$.
×