A particle moves according to the equation dvdt = α

Discussion Forum : Motion In One Dimension

Question -

A particle moves according to the equation $\frac{d v}{d t}$ = $α$ - $β$ v , where $α$ and $β$ are constants. Find the velocity as a funtion of time. Assume body starts from rest.

Options:

A . v = (

\frac{β}{α}

) (1 -

e^{- β t}

)

B . v = (

\frac{β}{α}

) (

e^{- β t}

)

C . v = (

\frac{α}{β}

) (1 -

e^{- β t}

)

D . v = (

\frac{α}{β}

) (

e^{- β t}

)

Answer: Option C
:
C

Take the relation given for acceleration and integrate with the given limits to obtain the desired function for velocity.

$\frac{d v}{d t}$ = $α$ - $β$ v $\Rightarrow$ $v \int 1$ $\frac{d v}{α - β v}$ = $t \int 0$ dt

v = ( $\frac{α}{β}$ ) (1 - $e^{- β t}$ )

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