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 meter. If the body is at rest at point $(6m,4m)$ 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 $2\text{s}$

When it will cross $y-$axis at that time x will be zero
As we know, $-\frac{\partial U}{\partial x}=F_x$
$U=6x+8y$ (given)
$F_x=-6$
as, $F_x=m{a}_x\Rightarrow a_x=\frac{-6}{2}=-3m/s^2$
By second equation of motion,
$s=ut+\frac{1}{2}a{t}^2$
$0-6=0-\frac{1}{2}\times 3\times t^2$
$t=2s$