Question

The potential energy (in joule) of a body of mass $2\text{kg}$ moving in the $x-y$ plane is given by $U=6x+8y$, where the position coordinates $x$ and $y$ are measured in metres. The body is at rest at point $(6\text{m},4\text{m})$ at time $t=0$. It will cross the $y-$ axis at time $t$ equal to

• A. $1\text{s}$
• B. $2\text{s}$
• C. $3\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is B $2\text{s}$

Given $U=6x+8y$
$F=\frac{-dU}{dx}\hat{i}+\frac{-dU}{dy}\hat{j}$
$=-6\hat{i}-8\hat{j}$ ;
$a_x=\frac{F_x}{m}=-3{\text{m/s}}^2$

Given, initial x coordinate $x_i=6$
When it crosses the $y-$ axis, $x$ coordinate is zero.
i.e $x_f=0$,
$s_x=x_f-x_i=-6\text{m}$

Applying 2nd eqn of motion in the $x-$ direction:
$s_x=u_{x}t+\frac{1}{2}{a}_x{t}^2$
$-6=\frac{1}{2}\times \frac{(-6)}{2}{t}^2=0\Rightarrow t=2\text{s}$