Question

A particle of mass 1 kg is moving in the $x-y$ plane and its potential energy $U$ in joule obeys the law $U=6x+8y$, where ($x,y$) are the coordinates of the particle in meter. If the particle starts from rest at (9,3) at time $t=0$, then

• A. Magnitude of acceleration of particle is $10m/s^2$
• B. Acceleration of particle is zero
• C. The particle crosses the y.axes at time $t=\sqrt{3}$ sec.
• D. The speed of the particle when it crosses y axes is $10\sqrt{3}m/s$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Magnitude of acceleration of particle is $10m/s^2$
C The particle crosses the y.axes at time $t=\sqrt{3}$ sec.
D The speed of the particle when it crosses y axes is $10\sqrt{3}m/s$

$U=6x+8y$
$\overrightarrow{F}=-6\hat{i}-8\hat{j};\overrightarrow{a}=-6\hat{i}-8\hat{j}$
$\left|\overrightarrow{a}\right|=10m/s^2$
$S_x=u_{x}y+\frac{1}{2}{a}_x{t}^2;-9=0-\frac{1}{2}\left(6\right)t^2$
$t=\sqrt{3}sec$
$\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t$
$\overrightarrow{v}=0+(-6\hat{i}-8\hat{j})\sqrt{3}$
$\left|\overrightarrow{v}\right|=10\sqrt{3}m/s$