A particle of mass m falls from rest through a resistive medium having resistive force, , where v is

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A particle of mass m falls from rest through a resistive medium having resistive force, , 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

$M \cdot \frac{dv}{dt} = mg - kv$$$\begin{matrix} & \ \int_{0}^{v}\mspace{2mu}\mspace{2mu}\frac{dv}{mg - kv} = \int_{0}^{t}\mspace{2mu}\mspace{2mu}\frac{dt}{	ext{ }m} \ & \frac{- 1}{k}ln\left( \frac{mg - kv}{mg} ight) = \frac{t}{	ext{ }m} \ & v = \frac{mg}{k}\left( 1 - e^{- kt/m} ight) \end{matrix}$$

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