Terminal Velocity & Drag Force – AP Physics C

Learning Objectives

Determine terminal velocity ($v_t$) when $F_{net} = 0$.

Compare linear drag ($F_D \propto v$) vs quadratic drag ($F_D \propto v^2$).

Analyze exponential velocity-time curves derived via differential equations.

Key Equations

Linear Drag Model:

$ m\frac{dv}{dt} = mg - bv $

$ v_t = \frac{mg}{b} $

Quadratic Drag Model:

$ m\frac{dv}{dt} = mg - cv^2 $

$ v_t = \sqrt{\frac{mg}{c}} $

Why It Matters

In AP Physics C, drag is the primary reason why Newton's Laws must be integrated. The opposing force scales dynamically with the object's velocity until $F_{drag}$ perfectly cancels $F_{gravity}$.