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Gravity Velocity Equations for Falling Objects
by Ron Kurtus (revised 9 August 2010)
An object dropped from some height has an initial velocity of zero (vi = 0). Simple equations allow you to calculate the velocity an object falls after a given period of time and the velocity it reaches a given distance. It is assumed that air resistance is negligible. The mass of the object is not a factor in these equations.
Questions you may have include:
- What is the equation for the velocity for a given time?
- What is the equation for the velocity to reach a given distance?
- What are some examples of these equations?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Velocity for a given time
You can determine the object's velocity according to the time it has fallen by the equation:
v = gt
where
- v is the vertical velocity of the object in meters/second (m/s) or feet/second (ft/s)
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
- t is the time in seconds (s) that the object has fallen
(See Derivation of Velocity-Time Gravity Equations for details of the derivations.)
Velocity of a falling object as a function of time or distance
Velocity for a given distance
The equation for the velocity of a falling object after it has fallen a certain distance is:
v = √(2gy)
where
- √(2gy) is the square root of the quantity (2gy)
- y is the vertical distance from the starting point in meters (m) or feet (ft)
(See Derivation of Velocity-Distance Gravity Equations for details of the derivations.)
Examples
The following are examples to illustrate application of the equations.
For a given time
What will be the velocity of an object after it falls for 3 seconds?
Solution
Substitute in the equation:
v = gt
If you use g = 9.8 m/s2, v = (9.8 m/s2)*(3 s) = 29.4 m/s.
If you use g = 32 ft/s2, v = (32 ft/s2)*(3 s) = 96 ft/s.
For a given distance
What is the velocity of an object after it has fallen 100 feet?
Solution
Since y is in feet, g = 32 ft/s2. Substitute in the equation:
v = √(2gy)
v = √[2*(32 ft/s2)*(100 ft)]
v = √(6400 ft2/s2)
v = 80 ft/s
Summary
There are simple equations for falling objects that allow you to calculate the velocity the object reaches for a given distance or time. The equations are:
v = gt
v = √(2gy)
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Resources
The following resources provide information on this subject:
Websites
Acceleration due to Gravity Calculations - from Western Washington University
Gravity and Gravitation Resources
Books
Top-rated
books on Simple Gravity Science
Top-rated
books on Advanced Gravity Physics
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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Gravity Velocity Equations for Falling Objects