Derivation Of A Function For Velocity For Falling Objects With Non-Negligible Air Resistance

Author: Leonhard Nagel

We all know what the velocity of a free-falling object is, when air resistance is negligible. But what if it's not negligible?

Abstract

For many falling objects, air resistance is assumed to be negligible; however, this assumption is not a valid one to make in many cases. Thus, a function relating velocity to time, under consideration of drag, can be used to better estimate the velocity of a falling object. In an idealized sense, two forces act upon a falling object: weight and drag. These two forces can be assumed to act in opposite direction to each other. This means that a simple equation for acceleration based on Newton’s second law of motion can be found, which can then be manipulated to yield an expression for velocity.

Derivation