Terminal Velocity Simulation: Drag Force
Drag Force: How a falling object finds its terminal velocity
Drag grows with the square of speed: D = ½CρAv². At release, v = 0, so D = 0 and the ball accelerates at the full g = 9.8 m/s². As v builds, drag climbs fast — doubling v quadruples D — so acceleration shrinks and the v–t curve bends. It is never a straight line after t = 0.
Terminal velocity is dynamic equilibrium, not a speed limit. When drag grows until D = mg, the net force is zero, so a = 0 and v stops changing: vₜ = √(2mg/CρA). The ball keeps falling at constant velocity — forces balanced, motion unchanged (Newton’s first law in action). On the Drag vs Speed graph, vₜ is exactly where the drag parabola crosses the mg line — watch the sliding dot chase that intersection.
Change a parameter mid-fall and the ball re-negotiates its equilibrium. Halve A and vₜ rises by √2 — drag momentarily loses to weight and the ball speeds up toward the new vₜ (a skydiver pulling into a dive). Enlarge A so that v > vₜ and drag exceeds weight: the ball keeps falling but slows toward vₜ from above — acceleration points upward while velocity still points down.
Terminal Velocity Simulation: Drag Force for AP Physics 1
Terminal velocity is the constant speed a falling object reaches when the upward drag force grows equal to the downward force of gravity, making the net force and the acceleration zero. The drag force on an object moving through air is D = ½CρAv², where C is the drag coefficient, ρ is the air density, A is the cross-sectional area, and v is the object's speed. Because drag grows with the square of speed, every falling object is heading toward a built-in equilibrium: vₜ = √(2mg/CρA).
This free interactive simulation lets you watch that equilibrium happen — and disturb it. A ball falls from rest while you track four live views at once: the force arrows on the ball (weight mg constant, drag D growing with v²), the v–t curve bending toward the vₜ asymptote, the a–t curve decaying from 9.8 m/s² to zero, and a Drag vs Speed graph where terminal velocity appears as the exact point where the drag parabola crosses the mg line.
Frequently asked questions
Q. How can a skydiver have zero acceleration while still falling fast?
A. Zero acceleration means velocity has stopped changing, not that motion has stopped. At terminal velocity, drag exactly balances weight, so the net force is zero and the skydiver continues downward at a constant speed — Newton's first law in action.
Q. Why does a heavy ball fall faster than a light one in air, but they land together in a vacuum?
A. Terminal velocity equals √(2mg/CρA), so a heavier object of the same shape and size has a higher terminal velocity — a lead ball beats a tennis ball through air. In a vacuum there is no drag, so every object accelerates at g and they land together. Try it: raise m in the simulation and watch vₜ climb.
Q. Is the drag force formula D = ½CρAv² on the AP Physics 1 equation sheet?
A. No. When an exam question needs it, the formula is given in the problem. What the exam actually tests is Newton's-laws reasoning: identifying the forces, explaining why acceleration decreases as speed increases, and sketching the v–t and a–t graphs of the approach to terminal velocity.
Q. What's the difference between air resistance and kinetic friction?
A. Kinetic friction is roughly independent of speed. Drag grows with the square of speed — doubling your speed quadruples the drag. That speed dependence is exactly why terminal velocity exists: the faster you fall, the harder the air pushes back, until it pushes back exactly as hard as gravity pulls.
Q. Why does the drag force keep getting bigger while the ball falls?
A. Drag depends on speed: D = ½CρAv². As gravity speeds the ball up, v² grows, so D grows. The growth is self-limiting — once D equals mg, acceleration hits zero, the speed stops increasing, and drag stops growing. Watch the sliding dot chase the intersection point on the Drag vs Speed graph.
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