A particle of mass m falls from rest through a resistive medium having resistive force, F = −kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents v

Question

A particle of mass m falls from rest through a resistive medium having resistive force, F = −kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?

Accepted Answer

Answer: (1) — Equation: mdv/dt = mg − kv Solution: v = (mg/k)(1 − e^(−kt/m)) So velocity increases from 0 and approaches terminal velocity asymptotically ⇒ graph (1)

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