As an object falls, its speed increases because it’s being pulled on by gravity. The acceleration of gravity near the earth is g = -9.81 m/s^2. To find out something’s speed (or velocity) after a certain amount of time, you just multiply the acceleration of gravity by the amount of time since it was let go of. So you get: velocity = -9.81 m/s^2 * time, or V = gt. The negative sign just means that the object is moving downwards. If it were positive, then it would be moving up. For speed rather than velocity, you just drop the negative sign.
If you have an initial velocity (if you threw the ball up or down instead of just letting go of it), then you have to include this in the equation, too, giving you: V = Vo + gt, where Vo is the initial velocity of the object. This equation will still work if you threw the ball to the side, instead of straight up or down, except that it will only give you the up-down velocity, not the total velocity. (And the number you should use for Vo is still just the up-down velocity that the object starts with.)
(republished on 07/11/06)
(published on 08/11/09)