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Overview of Gravity Equations for Objects Projected Upward
by Ron Kurtus (revised 17 August 2009)
When you throw or project an object upward, it slows down from its initial velocity until it reaches its peak. Then it falls back down to the ground. Given that initial velocity, you can calculate the velocity, distance and time of the object during its flight.
The equations for velocity, distance and time of the object depend on the direction of motion and position above or below the starting point.
Since the direction of the force of gravity is typically considered positive, we consider downward—toward the ground—as a positive direction and upward as a negative direction. Thus, downward velocities are positive and upward velocites are negative. Likewise, distances below the starting point are positive numbers and those above the starting point are negative.
Note: Some textbooks consider up as positive and down as negative. We feel it is more logical to consider an object that is accelerating downward to have a positive velocity. However, you need to be aware of what convention is being used when working from a book.
This lesson is an overview of the equations and has references to the other lessons that have the details.
Questions you may have include:
- What are the equations for velocity?
- What are the equations for distance?
- What are the equations for time?
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 equations
The equations for the velocity of an object projected upward at an initial velocity vi are:
v = gt + vi
v = ±√(2gx + vi2)
(See Gravity Velocity Equations for Objects Projected Upward for details.)
Distance equations
The equations for the distance from the starting point of an object projected upward at an initial velocity vi are:
x = (v2 − vi2)/2g
xmax = −vi2/2g (distance to peak or maximum height)
x = gt2/2 + vit
(See Gravity Distance Equations for Objects Projected Upward for details.)
Time equations
The equations for the time an object projected upward at an initial velocity vi travels are:
t = (v − vi)/g
t = [−vi ± √(vi2+ 2gx)]/g
(See Gravity Time Equations for Objects Projected Upward for details.)
Summary
When you project an object upward, its equations for velocity, distance and time depend on the direction of motion and position above or below the starting point.
We consider upward velocity to be negative and downward to be positive. Likewise, distances above the starting point are negative and below are positve numbers.
This lesson is an overview of the equations for objects projected upward and has references to the other lessons that have the details.
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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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Overview of Gravity Equations for Upward Motion