Drag and Terminal Velocity

A falling object experiences weight downwards, drag opposing relative motion and often upthrust upwards. At release from rest, drag is small; the downward resultant gives acceleration. As speed rises, drag increases and acceleration decreases.

At terminal velocity, upward drag plus upthrust equals weight and the resultant is zero. The object continues at constant speed. In a liquid, upthrust may be significant and should not automatically be ignored; in air it is often small compared with the weight of a dense object.

A speed–time graph approaches a horizontal terminal-speed level while its gradient decreases towards zero. An acceleration–time graph falls towards zero. Displacement continues increasing: terminal speed is not a stationary position.

Increasing cross-sectional area usually increases drag at the same speed and lowers terminal speed for otherwise unchanged conditions. Fluid density, shape and surface properties also matter. A denser or heavier object need not have a lower terminal speed: compare the full force balance and the changed geometry rather than only one factor.

In a suitable supervised experiment, allow a ball to settle into steady motion in a viscous fluid before timing it between two reference marks. Use several lower sections to check that equal distances take similar times. Measure separation along the direction of travel and keep viewing perpendicular to reduce parallax.

For falling paper cones in air, keep shape and area controlled when varying mass, and use a sufficiently long fall or video analysis to identify the steady-speed region. Repeated timings estimate scatter; temperature control matters because liquid viscosity changes with temperature. Avoid timing the initial accelerating region as though it were terminal motion.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.