What Is Terminal Velocity?

Terminal velocity is the constant velocity reached by an object moving through a fluid when the resultant force on it becomes zero. At this point, its acceleration is zero, although the object continues moving.

How Terminal Velocity Is Reached

Consider an object falling vertically through air:

1. Immediately after release, its speed is zero, so fluid resistance is negligible. Its weight acts downward, producing a downward resultant force and acceleration.
2. As the object speeds up, upward fluid resistance increases. The resultant downward force therefore decreases, so the object's acceleration becomes smaller.
3. Eventually, the upward forces balance the downward weight. Newton's second law gives

$$F_{\text{resultant}} = ma = 0$$

Therefore, $a=0$, and the object continues downward at a constant velocity called terminal velocity.

More precisely, an object falling through a fluid may experience both drag and buoyancy upward. At terminal velocity,

$$mg = F_{\text{drag}} + F_{\text{buoyancy}}$$

If buoyancy is negligible, this simplifies to $mg=F_{\text{drag}}$. For an $80\,\text{kg}$ skydiver, the weight is $80\times 9.8=784\,\text{N}$. Terminal velocity is reached when the total upward force is also .

Terminal velocity depends on the object's mass, shape, cross-sectional area, and the fluid's density and viscosity. A parachute increases area and drag, so balance occurs at a lower speed. Terminal velocity can therefore change if the object's orientation or surrounding fluid changes.

A common misconception is that no forces act at terminal velocity. The forces still act, but they are balanced, so the resultant force is zero.

IB Exam Technique

This is assessed at both SL and HL in A.1 Kinematics. For an Explain question, link increasing speed to increasing fluid resistance, decreasing resultant force, zero acceleration, and finally constant velocity. Do not say that terminal velocity means the object has stopped.