What formula can be used to determine the velocity of an object in free fall?

Assuming that you're given either an initial or final velocity, you can use the following equation and solve for the initial or final velocity. 

Vyf² = Vyi² - 2g(y - y₀)

Where, 
Vyf² = final velocity
Vyi₂² = initial velocity
g = 9.81 m/s²
(y - y₀) = the change in the distance along the y-axis.

You'll need also determine the positive and negative of your y-axis for your final solution because velocity can be positive or negative based on direction. Lastly, don't forget to square root both sides of your equation for your velocity. 

I hope this helps.