Free Fall Stokes vs Quadratic Drag

What you are seeing: three identical balls dropped from the same height at $t = 0$ . The yellow one experiences no drag (vacuum, $\dot v = -g$ ); the cyan one experiences Stokes drag ( $\dot v = -g - b v$ , linear in velocity); the orange one experiences quadratic drag ( $\dot v = -g - c |v| v$ ). They land at different times and arrive with different velocities.

The lower plot tracks $|v(t)|$ for each ball. Vacuum is a straight line $|v| = g t$ . Stokes asymptotes to its terminal $v_t = mg/b$ exponentially. Quadratic asymptotes to $v_t = \sqrt{mg/c}$ on a slower-than-exponential approach (think $\tanh$ shape). Crossover between the two drag laws happens at $v_c = b/c$ : above this speed quadratic drag dominates, below it Stokes dominates.

Figure 1. Free fall under three drag laws. Method: RK4 at dt = 1/240.

y_0 (m)120

b (Stokes)0.50

c (quad)0.050

WHAT TO TRY

Watch the vacuum ball pull ahead: with no drag it never stops speeding up, while the two drag balls settle into a steady fall.
In the speed plot, the drag curves flatten onto their dashed terminal-velocity lines; the vacuum line keeps climbing straight.
Raise the drag coefficients $b$ and $c$ and the terminal velocities drop, so the balls reach their steady speed sooner and lower.