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what is the formula for the speed of a falling object?
As an object falls, its speed increases because itís being pulled on by gravity. The acceleration of gravity is g = -9.81 m/s^2. To find out somethingís 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: speed = -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.
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 speed, not the total speed. (And the number you should use for Vo is still just the up-down velocity that the object starts with.)
(published on 10/22/2007)
Follow-Up #1: Time of fall?
How does one determine the time and velocity of a fall if you only have the distance of the fall?
Bothell, WA, USA
Well you need one more fact, the acceleration. If you are at the surface of the earth the acceleration is g = 32.2 feet/sec2
or 9.8 meter/sec2
. Integrating the acceleration once gives V = Vo
+ g T where Vo
is the initial velocity, presumably zero, and T is the time of fall. Integrating once more gives d = Vo
T + gT2
/2. So taking Vo
= 0 you get
T = sqrt(2d/g) and V=sqrt(2dg).
That V Lee gives is the final V. In case you want the average V over the fall, it's half that. Mike W.
(published on 08/11/09)
Follow-up on this answer.