Problem 1.69

A bar of mass $m$ resting on a smooth horizontal plane starts moving due to the force $F=m g / 3$ of constant magnitude. In the process of its rectilinear motion the angle $\alpha$ between the direction of this force and the horizontal varies as $\alpha=a s,$ where $a$ is a constant, and $s$ is the distance traversed by the bar from its initial position. Find the velocity of the bar as a function of the angle $\alpha$.