Derivation of Free Fall Equations

Rectilinear motion with constant acceleration is introduced early in physics courses. While there are many cases of this type of motion, we can consider free fall one of the best examples of the relationship among position, velocity and acceleration (click here). It is even more important, since it shows how physics and calculus go hand in hand. Therefore, we will observe how to derive three of the equations for this special case.

Free fall is simply the motion of a falling object under the influence of acceleration due to gravity, g, which is considered a constant. Therefore, we will start with the acceleration function and then apply integration to get the velocity and position as functions of time. The procedure is shown below:

Finally, we rewrite the equations in the most common form that appears in most textbooks for consistency.