--- title: "Drag and Terminal Speed from the Equation of Motion" description: "A drag force that grows with speed makes acceleration depend on velocity, and solving that equation gives an approach to a terminal speed. Linear and quadratic drag give different curves and different" canonical: https://lightmysky.com/learn/science/drag-and-terminal-speed-from-the-equation-of-motion-mt_In6VeoADzZ source: https://lightmysky.com/learn/science/drag-and-terminal-speed-from-the-equation-of-motion-mt_In6VeoADzZ.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Drag and Terminal Speed from the Equation of Motion A drag force that grows with speed makes acceleration depend on velocity, and solving that equation gives an approach to a terminal speed. Linear and quadratic drag give different curves and different terminal values. Subject: Science · Area: Forces & Motion · Ages 18 to 19 Page: https://lightmysky.com/learn/science/drag-and-terminal-speed-from-the-equation-of-motion-mt_In6VeoADzZ ## Ready when they can - Sets up the equation of motion for a body falling with linear or quadratic drag - Finds terminal speed by setting the acceleration to zero and says what that means physically - Sketches the velocity-time curve and explains why it flattens rather than crosses the terminal value ## Lesson: Falling against the wind Drag always pushes opposite your motion through air or water. Move your hand faster and the push grows. Tilt your hand edge on and the push shrinks, because less area faces the flow. For fast, large things the drag grows with speed squared: half C rho A v squared. C captures the shape, A is the facing area, and rho is the fluid density. For tiny, slow drifters like dust or bacteria, drag simply grows with speed itself. **Example.** A falling skydiver speeds up until drag equals weight, and then the net force is zero. From there the speed holds steady at the terminal value. A 75 kg diver headfirst reaches about 98 meters per second, while an 85 kg diver spread out floats down near 44 meters per second. **Tip.** To find terminal speed, set acceleration to zero in the equation of motion and solve. On a speed graph the curve rises steeply, then flattens as it nears the terminal line. It approaches from below and never crosses it. **Recap.** Drag grows with speed until it cancels weight, and then you fall steady at terminal speed. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Newton's Second Law as a Differential Equation](https://lightmysky.com/learn/science/newtons-second-law-as-a-differential-equation-mt_LzSNSkEovH) ## Opens up - [Viscosity, Poiseuille Flow and the Reynolds Number](https://lightmysky.com/learn/science/viscosity-poiseuille-flow-and-the-reynolds-number-mt_-1sWgkRtMs) - [Work as a Line Integral Along a Path](https://lightmysky.com/learn/science/work-as-a-line-integral-along-a-path-mt_UFuQUPGAt7)