Question 49 of 210

Which of the following option correctly describes the variation of the speed $υ$ and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force $F=-kυ$ , where 'k' is a constant, on the body? (Graphs are schematic and not drown to scale)

ABCD

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Answer: (C)

$\text{a}=\text{(g}-\alpha \text{v)}$

$\dfrac{\text{dv}}{\text{dt}}=$$\text{g}-\alpha \text{v}$

$\int _{0}^{\text{v}}\dfrac{\text{dv}}{\text{g}-\alpha \text{v}}=\int _{0}^{\text{t}}\text{dt} \Rightarrow \ell \text{n}\left(\dfrac{\text{g}-\alpha \text{v}}{\text{g}}\right)=-\alpha \text{t}$

$v={\text{v}}_{0}\left(1-{\text{e}}^{-\alpha \text{t}}\right) \text{a}=\dfrac{\text{dv}}{\text{dt}}={\text{v}}_{0}\alpha {\text{e}}^{-\alpha \text{t}}={\text{a}}_{0}{\text{e}}^{-\alpha \text{t}}$