Terminal Velocity
Gives the constant (maximum) falling speed reached when drag exactly balances gravity
The equation
What it solves
Gives the constant (maximum) falling speed reached when drag exactly balances gravity. For linear drag: v_t = mg/b; for quadratic drag: v_t = √(2mg/(ρC_d A)).
When to use it
Falling-object problems where you need the asymptotic speed or want to verify whether a given speed is close to terminal. Also sets the velocity scale for the transient decay toward terminal speed.
When NOT to use it
Terminal velocity is the long-time limit; do not use it for the instantaneous speed just after release. The formulas assume constant g and fluid density — invalid for very high altitudes or non-vertical falls where the drag direction changes.
Common mistakes
Using the linear formula for macroscopic objects (skydivers) instead of the quadratic formula. Solving mg = bv² (linear b times v²) — units must be checked carefully. Forgetting that terminal velocity depends on mass, so two objects of different mass and the same size reach different terminal speeds.