Drag and terminal velocity

When an object falls through a fluid such as air or water, gravity pulls it downward while the surrounding fluid exerts a drag force that opposes its motion, directed upward for a falling object. Crucially, drag force is not constant — it grows with the object's speed, so a slow-moving object experiences little drag while a fast-moving one experiences much more.

At the instant an object is released from rest, its speed is zero, so drag is also essentially zero, and gravity is the only significant force acting; the object accelerates downward at close to the free-fall acceleration g. As it speeds up, the growing drag force starts to subtract from the net downward force, so the acceleration itself decreases, though the object is still speeding up. This continues — accelerating, but at an ever-decreasing rate — until the drag force has grown large enough to exactly equal the object's weight. At that point the net force on the object is exactly zero, and by Newton's second law, zero net force means zero acceleration: the object stops speeding up and continues falling at a constant speed, called its terminal velocity.

Terminal velocity is not a state where all forces vanish; gravity and drag are both still fully present and acting on the object, just now equal in magnitude and opposite in direction, so they cancel. Which speed counts as "terminal" depends on the object's weight and on how drag force depends on speed for the object's size, shape, and the fluid involved — a skydiver in a spread-eagle position reaches a lower terminal velocity than the same person falling head-first, because the larger cross-sectional area in the spread-eagle position produces more drag at any given speed, so equilibrium with gravity is reached sooner, at a lower speed. This is also why a raindrop reaches a modest, survivable terminal velocity rather than continuing to accelerate all the way to the ground under gravity alone.