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Question

A locomotive of mass m starts moving so that its velocity varies according to the law v=αs, where α is constant and s is the distance covered. Find the total work done by all the forces acting on the locomotive during the first t seconds after the beginning of motion.

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Solution

The velocity is given as,

v=αs

dsdt=αs

x0dsαs=t0dt

2sα=t

s=α2t24

The acceleration is given as,

a=vdvds

=αs×α2s

=α22

The total work done is given as,

W=m×a×s

=m×α22×α2t24

=mα4t28

Thus, the total work done by all forces acting on the locomotive is mα4t28.


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