SfC Home > Physical Science > Physics >
Explanation of Gravity Velocity Equations for Falling Objects - Succeed in Understanding Physics. Also refer to physical science, force, mass, gravitational constant, acceleration, velocity, distance, time, calculation, square-root, Ron Kurtus, School for Champions. Copyright © Restrictions
Gravity Velocity Equations for Falling Objects
by Ron Kurtus (16 August 2009)
You can calculate the velocity an object falls after a given period of time or until it reaches 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 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 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
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 = √(2gx)
where
- √ stands for square root
- √(2gx) is the square root of the quantity (2gx)
- x is the distance from the starting point in meters (m) or feet (ft)
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 x is in feet, g = 32 ft/s2. Substitute in the equation:
v = √(2gx)
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 = √(2gx)
See the Side Menu for more Gravitation and Gravity topics
Be a champion
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.
What do you think?
Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible.
Share link
Feel free to establish a link from your website to pages in this site.
Or use our form to send this link to yourself or a friend.
Students and researchers
The Web address of this page is
www.school-for-champions.com/
science/gravity_equations_falling_velocity.htm.
Please include it as a reference in your report, document, or thesis.
Where can you go from here?
Gravity Velocity Equations for Falling Objects