Terminal Velocity and Air Resistance
Overview
When an object falls through a fluid, drag force increases with speed. Phase 1: F_drag < mg → net downward force → object accelerates. Phase 2: as speed increases, F_drag increases → acceleration decreases. Phase 3: F_drag = mg → F_net = 0 → constant maximum speed = terminal velocity. The v–t graph curves and flattens exponentially. Factors increasing terminal velocity: greater mass (more weight to overcome), smaller cross-section (less drag). Example: a skydiver face-down reaches ~55 m/s; head-down reaches ~90 m/s. A parachute dramatically increases drag area, reducing terminal velocity to ~5 m/s.
Air resistance and terminal velocity
When an object falls through air (or any fluid), drag force opposes motion. Drag increases with speed (roughly proportional to v²). Initially, drag is small and the object accelerates close to g. As speed increases, drag increases until it equals weight: W = F_drag. At this point, net force = 0, so acceleration = 0 — the object falls at constant terminal velocity. Skydivers reach terminal velocity of about 55 m/s face-down.
The v–t graph for terminal velocity
The v–t graph for a falling object with air resistance: the curve starts with slope = g (when v is small and drag is negligible), then the slope decreases as drag increases, and finally flattens to horizontal at terminal velocity. The acceleration (slope) decreases from g to 0 as drag builds up. If the parachute opens, the drag suddenly increases greatly, the object decelerates, and reaches a new, lower terminal velocity.
- ⚠Thinking terminal velocity means zero velocity — it means zero acceleration
- ⚠Forgetting that at terminal velocity, forces are balanced (not that forces have disappeared)