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Question

A body of mass m starting from rest is acted on by a force producing a velocity v=k×s where k is a constant and s is displacement. The work done by the force in the first t seconds is:

A
m2k2t28
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B
mk2t24
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C
mk2t28
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D
m2k2t4
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Solution

The correct option is C mk2t28
v=dsdt=(ks)12 .....(1)
s12ds=k12dt
Integrating both sides
s12=12k12t+constant
At t=0, s=0
constant=0
s12=12k12t
s=14kt2
Work done is equal to change in KE.
Δ(KE)=12mv2=12mks=12mk(14kt2)=mk2t28

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