A man moves along x axis such that velocity $v=\large\frac{1}{x}$. If he is initially at $x=2 m$ find the time when he reaches $x=4m$

$(a)\;6 sec\quad (b)\;4 sec \quad (c)\;3 sec \quad (d)\;he\;can't\;reach\; x=4m$

We have $v=\large\frac{dx}{dt}$
Therefore $\large\frac{1}{x}=\frac{dx}{dt}$
$\int dt=\int x dx$
$t= \large \frac{x^2}{2} \bigg|_2^4$
$=>t=6\;sec$
Hence a is the correct answer.

edited Jan 25, 2014 by meena.p