Question

# A particle moves according to the equation dvdt = α - β v , where α and β are constants. Find the velocity as a funtion of time. Assume body starts from rest.

A

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B

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C

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D

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Solution

## The correct option is D Take the relation given for acceleration and integrate with the given limits to obtain the desired function for velocity. dvdt = α - β v ⇒ v∫1 dvα−βv = t∫0 dt v = (αβ) (1 - e−βt)

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