Question

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

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

Answer 1

Answer: (D)

$10m/s$

Force along x-direction is =$F_x=\frac{-\delta u}{\delta x}=7\hat{i}$

Force along y- direction is: $F_y=\frac{-\delta u}{\delta 4}=24\hat{j}$

$\therefore \overrightarrow{F}=7\hat{i}+24\hat{j}$

$\overrightarrow{a}=\frac{\overrightarrow{F}}{m}=\frac{1}{5}(7\hat{i}+24\hat{j})$

at $t=2\sec$
$\overrightarrow{v}=u+at=0+\frac{1}{5}(7\hat{i}+24\hat{j})\times 2$
$\overrightarrow{v}=\frac{2}{5}(7\hat{i}+24\hat{j})$
$|\overrightarrow{v}|=\frac{2}{5}\sqrt{(49+576}$
$\frac{2}{5}\times 25=10m/s$.