Question

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

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

Answer 1

Answer: (D)

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