Answer
$v=\sqrt{\frac{4ax^{1.5}}{3m}}$
Work Step by Step
We know that the potential energy is the integral of the force with respect to distance, so we find:
$ U = \int (a\sqrt x)dx=\frac{2}{3}ax^{1.5}$
We know that the kinetic energy is equal to the change in potential energy. Thus:
$\frac{1}{2}mv^2 = \frac{2}{3}ax^{1.5}$
$v=\sqrt{\frac{4ax^{1.5}}{3m}}$
