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 :

Question

( A ) $t^{1/2}$
( B ) $t^2$
( C ) $t$
( D ) $t^3$