Overview of Gravity Equations for Objects Projected Downward

by Ron Kurtus (updated 29 May 2023)

When you throw or project an object downward, the object typically starts at zero velocity and is accelerated until it is released at some initial velocity.

The object then accelerates due to the force of gravity, with the initial velocity adding to the result of the acceleration. There are simple derived equations that allow you to calculate the velocity and displacement traveled, as well as the time taken to achieve a given velocity or displacement.

(See Overview of Gravity Equation Derivations for more information on derivations.)

Note: You normally do not need to memorize these equations, but you should know where to find them in order to solve equations.

This lesson is an overview of the equations and has references to the other lessons, which provide the details.

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 equations for the velocity of an object projected downward at an initial velocity of v_i are:

v = gt + v_i

v = √(2yg + v_i²)

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

Displacement equations

The equations for the displacement traveled of an object projected downward at an initial velocity of v_i are:

y = gt²/2 + v_it

y = (v² − v_i²)/2g

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

Time equations

The equations for the elapsed time of an object projected downward at an initial velocity of v_i are:

t = (v − v_i)/g

t = [−v_i + √(v_i²+ 2gy)]/g

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

Summary

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

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