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