Question

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by the equation, $U=-7x+24y$ Joule. Here x and y are in the meter at t=0, the particle is at the origin and moving with velocity $(2\hat{i}+3\hat{j})m/s$. The magnitude of acceleration of particle is

• A. $3$ $m/s^2$
• B. $5$ $m/s^2$
• C. $31$ $m/s^2$
• D. $15$ $m/s^2$

Answer 1

Answer: (B)

$5$ $m/s^2$

Given,

$m=5kg$

$u=-7x+24y$

$\overrightarrow{v}=2\hat{i}+3\hat{j}$

$F_x=-\frac{du}{dx}=7$

$F_y=\frac{du}{dy}=-24$

$|\overrightarrow{F}|=\sqrt{49+576}=25$

$a=\frac{F}{m}=\frac{25}{5}=5m/s^2$