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(D) Given displacement $S = \frac{t^2}{4}$.Velocity $v = \frac{dS}{dt} = \frac{d}{dt}\left(\frac{t^2}{4}\right) = \frac{2t}{4} = \frac{t}{2} \, m/s$.A

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$3$

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(D) Given displacement $S = \frac{t^2}{4}$.Velocity $v = \frac{dS}{dt} = \frac{d}{dt}\left(\frac{t^2}{4}ight) = \frac{2t}{4} = \frac{t}{2} \, m/s$.Acceleration $a = \frac{dv}{dt} = \frac{d}{dt}\left(\frac{t}{2}ight) = \frac{1}{2} \, m/s^2$.Force $F = m \cdot a = 6 	imes \frac{1}{2} = 3 \, N$.Work done $W = \int F \, dS = \int_0^2 F \cdot v \, dt = \int_0^2 3 \cdot \frac{t}{2} \, dt$.$W = \frac{3}{2} \int_0^2 t \, dt = \frac{3}{2} \left[ \frac{t^2}{2} ight]_0^2 = \frac{3}{4} [4 - 0] = 3 \, J$.

$A$ body of mass $6\,kg$ is under a force which causes displacement in it given by $S = \frac{t^2}{4}$ metres, where $t$ is time. The work done by the force in $2\,seconds$ is ............... $J$.

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