Question

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

• A. 5 m/s
• B. 14 m/s
• C. 175 m/s
• D. 10 m/s

Answer 1

Answer: (D)

$F=\frac{-\partial u \hat{i}}{\partial x} \frac{-\partial u \hat{j}}{\partial y} $
$=7 \hat{i}-24 \hat{j} $
$\therefore a_{x}=\frac{F_{x}}{m}=\frac{7}{5}=1.4\, m / s^{2}$
along positive $x-$ axis
$a_{y}=\frac{F_{y}}{m}=-\frac{24}{5}$
$=4.8\, m / s$ along negative y-axis
$\therefore v_{x}=a_{x} t=1.4 \times 2=2.8 \,m / s$
and $ v_{y}=4.8 \times 2=9.6 \,m / s $
$\therefore v=\sqrt{v_{x}^{2}+v_{y}^{2}}=10 \,m / s$