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# 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 (

**v**0).

_{i}=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.

(

See Overview of Gravity Equation Derivations for more information.)

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 = gt^{2}/2

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

y = v^{2}/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.

Check your numbers

## Resources and references

### Websites

**Falling Bodies** - Physics Hypertextbook

**Equations for a falling body** - Wikipedia

**Gravity Calculations - Earth** - Calculator

**Kinematic Equations and Free Fall** - Physics Classroom

### Books

**Top-rated books on Simple Gravity Science**

**Top-rated books on Advanced Gravity Physics**

## Questions and comments

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## Gravity Equations for Falling Objects