terminal velocity
Summary
Terminal velocity is the constant speed a falling object reaches in a fluid when the upward drag force (plus any buoyant force) equals its weight, so net force and acceleration are zero. Testable point: gravity still acts, but it is balanced, and greater viscosity lowers the terminal speed.
Detail
Meaning: As an object falls through a fluid, drag grows with speed while weight stays constant. At the speed where drag plus any buoyant force equals the weight, the net force is zero, so acceleration is zero and the object continues at constant velocity. On a velocity–time graph the curve rises, then flattens at a horizontal asymptote.
Equation: For a small sphere in a viscous fluid (Stokes' law, drag = 6πηrv): vt = 2r²(ρs − ρf)g / (9η). Here vt is terminal speed (m/s), r is radius (m), ρs and ρf are sphere and fluid densities (kg/m³), g is gravitational acceleration (9.8 m/s²), and η is viscosity (Pa·s).
On the MCAT: Expect a free-body diagram with weight down and drag and buoyancy up, or a graph of speed versus time. You may be asked to predict how terminal speed changes: it rises with a larger radius or a denser object and falls with higher fluid viscosity. A parachute raises drag and lowers terminal speed. The same balance describes particles settling in a fluid.
Common confusion: Students think gravity has stopped acting, or that zero net force means the object is at rest. Gravity still acts; drag cancels it, and zero net force means constant velocity, not zero velocity.
Sources
- Physics (Cutnell and Johnson)
- Physics for Scientists and Engineers (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.