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Question

A particle moves according to the equation dvdt=αβv where α and β are constants. Assuming particle starts from rest, it's velocity as a function of time will be

A
v=βα(1eβt)
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B
v=αβ(1eβt)
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C
v=βαeβt
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D
v=αβeβt
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Solution

The correct option is D v=αβ(1eβt)
dvdt=αβvdvdt=α{1βvα}dv(1βv/α)=αdtIntegratingbothsidesweget,ln(1βαv)×αβ=αt1βαv=eβtv=αβ(1eβt)

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