Newton's Laws & Forces

terminal velocity

Terminal velocity is the top speed a falling object reaches when air resistance grows strong enough to stop it speeding up any more. A skydiver does not fall faster and faster forever; after a while they fall at a steady maximum speed. That steady speed is the terminal velocity.

As an object falls, gravity pulls it down (weight m g) while air resistance pushes up, and drag grows with speed. Terminal velocity is reached when the upward drag exactly balances the downward weight, so the net force is zero and, by Newton's second law, the acceleration is zero. From then on the object falls at constant velocity. Setting drag equal to weight (for the v^2 drag law, k v^2 = m g) gives the terminal speed v_t = sqrt(m g / k), where k depends on size, shape, and air density.

A human skydiver in a belly-down spread reaches roughly 55 m/s (about 200 km/h); a parachute hugely increases the drag constant k, dropping the terminal velocity to a safe few m/s for landing. Raindrops, seeds, and dust all fall at their own small terminal velocities.

A skydiver speeds up at first, but around 55 m/s the air's drag equals their weight. Net force becomes zero, acceleration stops, and they fall at that steady terminal velocity, until the parachute opens and lowers it.

Terminal velocity is where drag balances weight and acceleration drops to zero.

Terminal velocity is not a property of the object alone: it depends on air density and the object's shape and area, which is why opening a parachute changes it dramatically. Without air (as on the airless Moon) there is no terminal velocity; everything just keeps accelerating.

Also called
終端速率