A body of mass $6 \mathrm{~kg}$ 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

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Aicharya · Accepted Answer

$m=6 \mathrm{~kg}, s=\frac{t^2}{4}$ Work done $(W)=$ Force $	imes$ Displacement $=m a 	imes s$ Displacement, $s=\frac{t^2}{4}$ $	herefore$ Acceleration, $a=\frac{d v}{d t}=\frac{d}{d t}\left(\frac{d s}{d t}ight)$ $=\frac{d}{d t}\left[\frac{d}{d t}\left(\frac{t^2}{4}ight)ight]=\frac{d}{d t}\left(\frac{2 t}{4}ight)=\frac{1}{2}$ $\begin{aligned} 	herefore \quad W & =6 	imes \frac{1}{2} 	imes \frac{t^2}{4}=\frac{3}{4} t^2=\frac{3}{4}(2)^2 \ & =\frac{3}{4} 	imes 4=3 \mathrm{~J}\end{aligned}$

A body of mass $6 \mathrm{~kg}$ is under a force which causes displacement in it given by $s=\frac{t^2}{4}$…

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