Q. The potential energy of a particle of mass 5 kg moving in the $x - y$ plane is given by $U = ( - 7x + 24y)$ J, $x$ and $y$ being in metre. If the particle starts from rest from origin then speed of particle at $t = 2$ s is
A) $5\ ms^{- 1}$
B) $01\ ms^{- 1}$
C) $17.5\ ms^{- 1}$
D) $10\ ms^{- 1}$
Explanation
(d) $F = - \frac{\partial U}{\partial x}\widehat{\mathbf{i}} - \frac{\partial U}{\partial y}\widehat{\mathbf{j}} = 7\widehat{\mathbf{i}} - 24\widehat{\mathbf{j}}$
$\therefore\ \ \ a_{x} = \frac{F_{x}}{m} = \frac{7}{5} = 1.4\ ms^{- 2}$ along positive $x$-axis
$a_{y} = \frac{F_{y}}{m} = - \frac{24}{5}$
$= 4.8ms^{- 2}$ along negative $y$-axis
$\therefore\ v_{x} = a_{x}t = 1.4 \times 2$
$= 2.8\ ms^{- 2}$
and $v_{y} = 4.8 \times 2 = 9.6\ ms^{- 1}$
$\therefore\ v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 10\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.