Resistive Forces

A resistive force pushes back against motion through a fluid. Air or water drag always points opposite the velocity, and it grows as the object speeds up, so it is nothing like a steady push. Take downward as positive and the fall obeys m·dv/dt = mg − bv for linear drag. Release it from rest and, as it speeds up, the drag climbs until it balances gravity, the net force drops to zero, and the speed levels off at the terminal velocity v_t = mg/b. Gravity has not changed along the way; only the net force has.

Drag punishes three assumptions. That it is a steady force, which invites constant-acceleration kinematics like v = v₀ + at — but the acceleration starts at g and falls toward zero as the object speeds up. That the equation of motion can be written loosely, dropping a sign or a term so drag adds to gravity instead of opposing it, or so the terminal velocity comes out negative. And that terminal velocity means zero force rather than zero net force — at terminal speed gravity still pulls with mg and the drag matches it at bv_t = mg, which is exactly why the speed holds steady.