AP® Physics C: Mechanics · Unit 2 · Topic 2.9
Drag and Terminal Velocity
Terminal velocity is the constant speed a falling object reaches when drag force grows large enough to exactly cancel gravity, making net force and acceleration zero.
A skydiver leaving a plane starts with zero velocity and accelerates downward near g, 9.8 m/s2. But air resistance isn't constant — it grows with speed. The faster she falls, the harder the air pushes back. So the net downward force shrinks as speed builds, and acceleration shrinks with it. She never stops accelerating at the start, but she accelerates less and less, approaching a limit rather than hitting it suddenly.
The mechanism is a simple force balance written as a differential equation. Gravity mg pulls down, drag Fd = bv (or kv2 for faster objects) pushes up, opposing motion. Newton's second law gives m(dv/dt) = mg - bv. As v grows, bv grows, and the right side shrinks toward zero. When bv finally equals mg, dv/dt = 0: velocity stops changing. That constant speed is terminal velocity, vt = mg/b for linear drag. The object keeps falling, but it stops speeding up.
This connects forward to the differential equation itself: solving m(dv/dt) = mg - bv gives velocity as an exponential approach to vt, not a sudden jump. It also connects back to Newton's second law and net force reasoning used throughout the unit — terminal velocity is just another equilibrium, like a block at rest under balanced forces, except here the object is moving at constant nonzero velocity instead of sitting still.
Key terms
- Terminal velocity
- The constant speed at which drag force exactly balances gravity, leaving zero net force and zero acceleration.
- Drag force
- A resistive force from a fluid like air that increases with speed and opposes the direction of motion.
- Net force
- The vector sum of all forces acting on an object, which determines its acceleration via Newton's second law.
- Linear drag
- A drag force model where resistance is proportional to speed, written Fd = bv.
- Quadratic drag
- A drag force model where resistance is proportional to speed squared, written Fd = kv2, common at higher speeds.
Watch it explained
- How it worksHow does a velocity-dependent drag force eat away the net force as speed builds?
- Worked exampleFind the terminal speed of a 75 kg skydiver whose drag force has magnitude 15v newtons.
- Common mistakeWhy doesn't an object at terminal velocity have any acceleration left over?
- Going furtherWhat changes about terminal speed when drag grows with the square of the speed instead?
Check yourself
End of topic.