Question

The potential energy $U$ of a particle of mass $m=1\text{kg}$ moving in $x-y$ plane is given by $U=3x+4y,$ where $x$ and $y$ are in metre and $U$ is in joule. If initially particle was at rest, then its speed at $t=2\text{s}$ will be

• A. $10\text{m/s}$
• B. $6\text{m/s}$
• C. $8\text{m/s}$
• D. $7\text{m/s}$

Answer 1

The correct option is A $10\text{m/s}$

Given $U=3x+4y,$
So $\frac{\partial U}{\partial x}=3$,$\frac{\partial U}{\partial y}=4$
We have relation between force and potential energy as
$\overrightarrow{F}=-\frac{\partial U}{\partial x}\hat{i}-\frac{\partial U}{\partial y}\hat{j}=-3\hat{i}-4\hat{j}$
$|\overrightarrow{F}|=\sqrt{3^2+4^2}=5\text{N}$
From Newtons second law
$ma=5$
$a=5{\text{ms}}^{-2}(m=1kg)$
As acceleration is constant we can apply equations of motion
$V=u+at$
$Att=2s,$
$V=0+5\left(2\right)=10{\text{ms}}^{-1}.$