Velocity w/axis vs without

Hi, quick question
I've just started to learn circular motion and i tried a basic force problem.

Imagine there is a ball on a string with a string length 'r', and a ball mass 'm'.
You apply a force 'F' for one second. Can the arc length of the ball's motion be calculated the same as linear motion? [itex]d=\frac{F{t^2}}{2m}[/itex] (replacing acceleration with F/m, v_i=0)
Can I also go as far as the find the angular velocity by dividing by the radius?
[tex]ω=\frac{F{t^2}}{2mr}[/tex]

Thanks.