DRAG
Terminal velocity: the truce between weight and air, one exponential.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A body falls through air that drags on it in proportion to speed: F_d = bv. Weight is constant; drag grows as the body accelerates. Does speed climb forever?
Forces
At release, v = 0 — drag hasn’t woken yet, and the body falls at the full g. But every gained m/s feeds the opposing force bv: the faster it falls, the harder the air pushes back.
Solve
Terminal velocity is the truce: set a = 0 and mg = bv_t, so v_t = mg/b. The time constant τ = m/b sets the pace — the whole approach is a single exponential.
Fall
Watch the gap close: v climbs steeply, then bends as drag claws back the acceleration. At t = τ the body has closed 63.2% of the gap to v_t. The curve leans on the asymptote but never touches.
Terminal
Five time constants in, the ledger is effectively settled: drag matches weight to within 0.7%, acceleration has all but vanished, and the fall is steady. Terminal — an equilibrium approached, never crossed.