Question

The potential energy (in SI units) of a particle of mass $2kg$ in a conservative field is $U=6x-8y$. If the initial velocity of the particle is $\overrightarrow{u}=-1.5\hat{i}+2\hat{j}$ then the total distance travelled by the particle in first two seconds is:

• A. 10 m
• B. 12m
• C. 15m
• D. 18m

Answer 1

The correct option is C 15m

$\overrightarrow{F}=-\frac{\partial U}{\partial X}\hat{i}-\frac{\partial U}{\partial Y}\hat{j}=-\left[6\hat{i}\right]+\left[8\right]\hat{j}=-6\hat{i}+8\hat{j}$
$\therefore \overrightarrow{a}=-3\hat{i}+4\hat{j}$ has same direction as that of
$\overrightarrow{u}=\frac{-3\hat{i}+4\hat{j}}{2}=\left(\frac{\overrightarrow{a}}{2}\right)$
$|\overrightarrow{a}|=5\Rightarrow |\overrightarrow{u}|=5/2$
Since $\overrightarrow{u}$ and $\overrightarrow{a}$ are in same direction, particle will move along a straight line
$\therefore s=ut+\frac{1}{2}a{t}^2=\frac{5}{2}\times 2+\frac{1}{2}\times 5\times 2^2=5+10=15m.$