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  4. The displacement x (in metre) of a particle of mass kg moving in one dimension under the action of a force is related to the time t (in seconds) by the equation: t=√x+3. The work done in first 6 seconds is:-

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Q. The displacement $x$ (in metre) of a particle of mass $kg$ moving in one dimension under the action of a force is related to the time $t$ (in seconds) by the equation: $t=\sqrt{x}+3.$
The work done in first 6 seconds is:-

NTA AbhyasNTA Abhyas 2020

Solution:

$x=t^{2}+9-6t$
so $v=2t-6$
Further, At $t=0v=2\times 0-6=-6$
At $t=6v=2\times 6-6=+6$
Initial $KE=\frac{1}{2}m\left(- 6\right)^{2}=18m$
Final $KE=\frac{1}{2}m\left(6\right)^{2}=18m$
Work done $=$ Change in $KE$
$W=18m-18m=0$