Question

# A body of mass $$'m'$$ starting from is acted on by a force producing a velocity $$v=\sqrt {k \times s}$$ where $$k$$ is a constant and $$s$$ is displacement .The work done by the force in the first $$'t'$$ seconds is:

A
m2 k2 t2/8
B
m k2 t2/4
C
m k2 t2/8
D
m2 k2 t/4

Solution

## The correct option is C $$m\ k^{2}\ t^{2}/8$$$$v=\sqrt{k\times s}$$$$\dfrac{ds}{dt}=\sqrt {k\times s}$$on integration we get$$s=\dfrac{kt^2}{4}$$differentiating with respect to t$$v=\dfrac{kt}{2}$$differentiating with respect to t$$a=\dfrac{k}{2}$$W=Fs=$$\dfrac{mk^2t^2}{8}$$Physics

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