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Gravity Time Equations for Falling Objects
by Ron Kurtus (16 August 2009)
You can calculate the time it takes for a falling object to reach a given velocity or to reach a given distance 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 time to reach a given velocity?
- What is the equation for the time 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.
Time to reach given velocity
The equation for the time it takes a falling object to reach a given velocity is:
t = v/g
where
- t is the time in seconds
- v is the velocity 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)
Elapsed time of a falling object as a function of velocity or distance
Time to fall given distance
The equation to determine the time it takes an object to fall a given distance is:
t = √(2x/g)
where
- x is the distance from the starting point in meters (m) or feet (ft)
- √ stands for square root
- √(2x/g) is the square root of the quantity (2x/g)
Examples
The following are examples to illustrate application of the equations.
Given the velocity
How long does it take for a falling object to reach 224 ft/s?
Solution
Since v is in ft/s, g = 32 ft/s2. Substitute values in the equation:
t = v/g
t = (224 ft/s)/(32 ft/s2)
t = 7 seconds
Given the distance
How long does it take for an object to fall 200 meters?
Solution
Since distance is in meters, g = 9.8 m/s2. Substitute values in the equation:
t = √(2x/g)
t = √[2*(200 m)/(9.8 m/s2)]
t = √(40.8 s2)
t = 6.39 s
Summary
There are simple equations for falling objects that allow you to calculate the time taken to achieve a given velocity or distance. These equations are:
t = v/g
t = √(2x/g)
See the Side Menu for more Gravitation and Gravity topics
Check your numbers
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 Time Equations for Falling Objects