Question

A particle is moving along $x-axis$ such that its velocity is $v=\frac{2}{x}$. If at $t=0,x=1m$ then the time when $x=2m$ is,

• A. $1s$
• B. $0.5s$
• C. $0.75s$
• D. $0.25s$

Answer 1

The correct option is C $0.75s$

We know that $v=\frac{dx}{dt}$ so using given expression we have $\frac{dx}{dt}=\frac{2}{x}$ or $xdx=2dt$ .....(1)

Integrating above equation both sides we get $\frac{x^2}{2}=2t+c$ ....(2)

where $c$ is the integration constant.

It is given that at $t=0,x=1$ so putting it in above equation we get $\frac{1}{2}=c$

so putting $c=0.5$ and $x=2$ in equation-2 we get $t=0.75s$

Option C is correct.