A particle of mass $2.0\ \text{kg}$ starts from rest at $x = 0$ at time $t = 0$ and moves along the $x$-axis. Its speed depends on its position as $v = \alpha\sqrt{x}$, with $\alpha = 3.0\ \text{m}^{1/2}\,\text{s}^{-1}$. Which of the following statements are correct?