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Gravity Distance Equations for Falling Objects
by Ron Kurtus (16 August 2009)
You can calculate the distance an object falls until it reaches a given velocity or after a given period of time from some simple equations. The assumption is that the objects are dropped and not accelerated up or down. Also, 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 distance to reach a given velocity?
- What is the equation for the distance for a given time?
- 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.
Distance for given velocity
The equation for the distance a falling object travels to reach a given velocity is:
x = v2/2g
where
- x is the distance from the starting point in meters (m) or feet (ft)
- v is the velocity in m/s or ft/s
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
Distance of a falling object as a function of velocity or time
Distance for a given time
The equation for the distance an object falls in a given time is:
x = gt2/2
where t is the time in seconds (s).
Examples
The following are examples to illustrate application of the equations.
Given the velocity
If v = 75 ft/s, how far has the object fallen?
Solution
Since v is in ft/s, g = 32 ft/s2. Substitute values in the equation:
x = v2/2g
x = (75 ft/s)*(75 ft/s)/2*(32 ft/s2)
x = (5625 ft2/s2)/(64 ft/s2)
x = 87.89 ft
Given the elapsed time
If t = 4 seconds and g = 9.8 m/s2, find the distance the object has fallen.
Solution
Substitute values in the equation:
x = gt2/2
x = (9.8 m/s2)*(16 s2)/2
x = 78.4 m
Summary
There are simple equations for falling objects that allow you to calculate the distance traveled for a given velocity or time. These equations are:
x = gt2/2
x = v2/2g
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Resources
The following resources provide information on this subject:
Websites
Acceleration due to Gravity Calculations - from Western Washington University
Gravitation and Gravity 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 Distance Equations for Falling Objects