The motion of a body falling from rest in a resistive medium is described by the equation d v d t = a - b v , where a and b are constants. The velocity at any time t is

d v d t = a - b v or ∫ 0 v d v a - b v = ∫ 0 t d t or - 1 b l o g a - b v 0 v = t or a - b v a = e - b t or a - b a v = e - b t v = a b ( 1 - e - b t )

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PhysicsKinematics1-DEasy2 minPYQ_2020

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The motion of a body falling from rest in a resistive medium is described by the equation $\frac{d v}{d t} = a - b v,$ where $a$ and $b$ are constants. The velocity at any time $t$ is

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Answer:

Solution:

$\frac{d v}{d t} = a - b v$

or $\int_{0}^{v} \frac{d v}{a - b v} = \int_{0}^{t} d t$

or $- \frac{1}{b} {[l o g (a - b v)]}_{0}^{v} = t$

or $(\frac{a - b v}{a}) = e^{- b t}$

or $a - \frac{b}{a} v = e^{- b t}$

$v = \frac{a}{b} (1 - e^{- b t})$

Stream:NTA_ABHYASSubject:PhysicsTopic:KinematicsSubtopic:1-D

⏱ 2mℹ️ Source: PYQ_2020

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