Velocity Functions with Air Resistance and Linear First-Order Differential Equations Explained

In A-Level Mathematics, students learn to solve linear first-order differential equations. One application of this appears in A-Level Physics (well, if you do AQA Option D: Turning Points). We can use Stokes’ Law for the fluid drag on a small spherical body moving through a viscous fluid. Stokes’ Law is used with Millikan’s experiment to determine the discrete unit of charge transferred on and off a droplet of oil. Maybe I’ll do a video about that in the future.

The video I have recorded today was prompted by me forgetting how to solve this whilst standing in front of a class of Year 12 students. Embarrassing! Hopefully this quick video remedies some of the embarrassment.

In the video, I derived the function for velocity dependent on time for a small falling spherical body. It requires knowledge of the chain rule and the product rule.

Anyway, here it is:

I recorded a video a few years back where I used Wolfram Alpha to help me solve a nonlinear first-order differential equation, but I want to do it again and solve it myself. Watch this space!