How do I derive an expression for the velocity vector for any α ?

[griffith]

Homework Statement

This question is part of a homework set. I have shown my attempt and would like help understanding the concepts involved.

Relevant Equations

md2/dt2(s) = Fcos(as)

A bar of mass m resting on a smooth horizontal plane starts
moving due to the force F of constant magnitude. In the
process of its rectilinear motion the angle α between the direction of
this force and the horizontal varies as α = as, where a is a constant,
and s is the distance traversed by the bar from its initial position.
Find the velocity vector of the bar as a function of the angle α. I have tried solving it for all α in the interval [0, inf] but I was only able to find the velocity vector for the angle α in the interval [0,pi/2].

 

[jedishrfu]

Please read our site guidelines regarding homework requests.

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[vela]

Find the velocity vector of the bar as a function of the angle α. I have tried solving it for all α in the interval [0, inf] but I was only able to find the velocity vector for the angle α in the interval [0,pi/2].

I assume you're troubled by the fact that when $\alpha > \pi$, the expression you derived gives you $v^2<0$.

When $\alpha = \pi$, what's the velocity of the bar and which way does the force point?

 

[griffith]

I assume you're troubled by the fact that when $\alpha > \pi$, the expression you derived gives you $v^2<0$.

When $\alpha = \pi$, what's the velocity of the bar and which way does the force point?

velocity equals 0 and the force vector would point to the left(wrt the pic i drew)