A particle located at $x = 0$ at time $t = 0$, starts moving along the positive $x$-direction with a velocity '$v$' that varies as $v = \alpha \sqrt{x}$. The displacement of the particle varies with time as\\
(1) $t^{3}$\\
(2) $t^{2}$\\
(3) $t$\\
(4) $t^{1/2}$