Gravity Equations for Falling Objects

by Ron Kurtus (updated 29 May 2023)

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_i = 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.

(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 = 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.

Check your numbers