1. Tardigrade
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  4. The potential energy of a particle of mass 5 kg moving in the x- y plane is given by, U=(- 7 x + 24 y) J where x and y being in metre. If the particle starts from rest from the origin, then the speed of the particle at t=2 s is :

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Q. The potential energy of a particle of mass $5 \, kg \, $ moving in the $x- \, y$ plane is given by, $U=\left(- 7 x + 24 y\right) \, J$
where $x$ and $y$ being in metre. If the particle starts from rest from the origin, then the speed of the particle at $t=2 \, s$ is :

NTA AbhyasNTA Abhyas 2022

Solution:

$\because \overset{ \rightarrow }{F}=-\left[\frac{\Delta U}{\Delta x} \hat{i} + \frac{\Delta U}{\Delta y} \hat{j}\right]=-\left[- 7 \, \hat{i} + 24 \, \hat{j}\right]$
$\therefore F=\sqrt{7^{2} + 2 4^{2}}=25 \, N\Rightarrow \, a=F/m=25/5=5 \, ms^{- 2}$
$\because v=u+at$
$=0+5 \, \times \, 2=10 \, ms^{- 1}$