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Acceleration

The accelerat...

Question

The acceleration of a particle is $a = a_{0} - b v$ , where $v$ is velocity at instant $t$ . If the particle starts from rest at $t$ =0, find the velocity of the particle as the function of time.

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Solution

$a = a_{0} - b v \frac{d v}{d t} = a_{0} - b v \int_{0}^{v} \frac{d v}{a_{0} - b v} \int_{0}^{t} d t \frac{- l n}{b} (a_{0} - b v) = t + l n C a_{0} - b v = e^{- b t} v = \frac{a_{0} - e^{- b t}}{b}$

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