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Gravity Velocity Equations for Objects Projected Downward
by Ron Kurtus (28 August 2009)
If you know the initial velocity that an object is thrown or projected downward, you can calculate its velocity when the object reaches a given distance from the starting point or when it reaches a given elapsed time. Some examples illustrate these equations.
The equations were determined from the Derivation of Gravity Equations and are summarized in Overview of Gravity Equations for Objects Projected Downward.
Note: You normally do not need to memorize these equations, but you should know where to find them in order to solve equations.
Questions you may have include:
- How do you find the velocity for a given distance?
- How do you find the velocity 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.
Velocity for a given distance
The equation for the velocity of an object that has been thrown downward after it has traveled a given distance is:
v = √(2gx + vi2)
where
- v is the velocity in meters/second (m/s) or feet/second (ft/s)
- √(2gx + vi2) is the square root of the quantity (2gx + vi2)
- x is the distance from the starting point in m or ft
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
- vi is the initial velocity of the object thrown downward
v, x and vi are all positive numbers.
Velocity of an object thrown downward as a function of
initial velocity and distance or
time
Velocity for a given time
The equation for the velocity of an object that has been thrown downward after it has fallen a given amount of time is:
v = gt + vi
where t is the time the object has fallen in seconds (s).
Examples
The following examples illustrate applications of the equations.
For a given distance
Find the velocity of a rock that is thrown down at 2 m/s after it has traveled 2 meters.
Solution
You are given that vi = 2 m/s and x = 2 m. Since vi is
in m/s and x is in m,
g = 9.8 m/s2. The equation to use is:
v = √(2gx + vi2)
Substitute values in the equation:
v = √[2*(9.8 m/s2)*(2 m) + (2 m/s)2]
v = √(39.2 m2/s2 + 4 m2/s2)
v = √(43.2 m2/s2)
v = 6.57 m/s
For a given time
Suppose you throw the object downward at 10 m/s. Find its velocity after 4 seconds.
Solution
You are given that vi = 10 m/s and t = 4 s. Since vi is in m/s, g = 9.8 m/s2. The equation to use is:
v = gt + vi
Substitute values in the equation:
v = (9.8 m/s2)*(4 s) + 10 m/s
v = 39.2 m/s + 10 m/s
v = 49.2 m/s
Summary
You can calculate the velocity when an object that is projected downward reaches a given distance from the starting point or when it reaches a given elapsed time from the equations:
v = √(2gx + vi2)
v = gt + vi
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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 Velocity Equations for Objects Projected Downward