Newton's second law states that $\vec F=m \vec a$ which is worth $m \vec g$ in this example.
Notice that $a(t)=v'(t)=r''(t)$ since it's a 1 dimensional problem. So $a(t)=g$.
Mathematically you have $g=\frac{dv}{dt}\Rightarrow g dt =dv$.
Try to take it from there. How would you go to find out $v(t)$?