Question

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

• A. 5 m / s
• B. 14 m / s
• C. 17.5 m / s
• D. 10 m / s

Answer 1

Answer: (D)

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