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Question

# A locomotive of mass m starts moving so that its velocity varies according to the law v=k√s where k is 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.

A
W=18mk4t2
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B
W=14m2k4t2
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C
W=14mk4t4
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D
W=18mk4t4
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Solution

## The correct option is A W=18mk4t2W.D by all forces = change in KE.Since v=k√SHence v2=k2S2vdvds=k2dvdt=k22⇒dv=k22dt⇒v=k22tW.D. by all forces =ΔKE=12mv2=12m(k22t)2=18mk4t2

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