Solving a Separable ODE for Terminal Velocity Kinematics

Differential Equations Differential Equations · Differential Equations — University

Question

A particle falls through air with acceleration given by $$a = \frac{g}{v_f^2}\left(v_f^2 - v^2\right)$$ where $g$ is gravitational acceleration and $v_f$ is the terminal velocity. The particle starts from rest. Determine the time $t$ needed for the velocity to reach $v = \dfrac{v_f}{2}$.

Step-by-step video solution

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