AP Physics C: Mechanics / Unit 2: Force and Translational Dynamics
2.9 Resistive Forces
Notes
Some forces depend on speed, such as air drag: $F=-bv$ (or $\propto v^2$ at high speed).
- Falling with drag: $\displaystyle mg-bv=m\frac{dv}{dt}$.
- Terminal velocity: when drag equals weight, $\displaystyle v_T=\frac{mg}{b}$.
- Solution from rest: $v(t)=v_T\left(1-e^{-bt/m}\right)$.
Practice
At terminal velocity, acceleration is:
Drag balances weight.
For $F_{drag}=bv$, terminal velocity is:
$mg=bv_T$.
Falling from rest with linear drag, $v(t)$:
Exponential approach.
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