# Gravity Equations for Falling Objects

by Ron Kurtus (revised 11 March 2017)

A falling object is an object that you drop from some height above the ground. Since it is simply dropped, its initial velocity is zero (vi = 0).

There are simple derived equations that allow you to calculate the velocity for a given time or displacement from the starting point, the displacement the object falls within a given time or when it has reached a given velocity, and the time it takes to reach a given velocity or displacement.

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:

• What are the velocity equations?
• What are the displacement equations?
• What are the time equations?

This lesson will answer those questions. Useful tool: Units Conversion

## Velocity equations

The equation for the velocity of a falling object over a given time is:

v = gt

The velocity of a falling object when it reaches a given distance or displacement is:

v = √(2gy)

(See Gravity Velocity Equations for Falling Objects for details on using these equations, as well as some examples.)

## Displacement equations

The equation for the displacement of a falling object over a given time is:

y = gt2/2

The displacement of a falling object when it reaches a given velocity is:

y = v2/2g

(See Gravity Displacement Equations for Falling Objects for details on using these equations, as well as some examples.)

## Time equations

The time a falling object takes to reach a given velocity is:

t = v/g

The equation for the time a falling object takes to reach given distance or displacement is:

t = √(2y/g)

(See Gravity Time Equations for Falling Objects for details on using these equations, as well as some examples.)

## Summary

There are simple equations for falling objects that allow you to calculate the velocity and displacement traveled, as well as the time taken to achieve a given velocity or displacement.

## Resources and references

Ron Kurtus' Credentials

### Websites

Gravity Resources

Falling Bodies - Physics Hypertextbook

Equations for a falling body - Wikipedia

Gravity Calculations - Earth - Calculator

Kinematic Equations and Free Fall - Physics Classroom

### Books

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