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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=18mk4t2Given v=k√s differentiating above equation dvdt=k2√s.dsdt a=k22 F=ma=mk22 (Distanced covered in t seconds) dsdt=v,∫x01v.ds=∫t0dt∫x01k√s.ds=∫t0dt2√xk=t⇒x=t2k24 Workdone during t seconds is ∫dW=∫x0F.ds=mk22∫t2k240ds=mk4t28

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