Question

See the photo and then tell me answer plzzz.

Answer 1

ANSWER....

$x = \frac{a}{b} (1 - {e}^{ - ct} ) \\ \\ differentiate \: the \: give \: equation \\ \\ \frac{dx}{dt} = \frac{d( \frac{a}{b}) }{ dt} - \frac{a}{b} (\frac{d( {e}^{ - ct} )}{dt}) \\ \\ \frac{dx}{dt} = 0 - \frac{a}{b} ({ - c \times {e}^{ - ct} } ) \\ \\ v = \frac{ac}{b} {e}^{ - ct} \\ \\ as \: we \: know \: {e}^{a} \: is \: always \: dimension \\ less \\ \\ so \\ dimension \: of \: velocity = dimension \: of \: \frac{ac}{b} \\ \\ dimension \: of \: \frac{ac}{b} = l. {t}^{ - 2}$

• CONCEPT USED...

$1. \: \: \: differential \: of \: any \: constant \: is \\ \: zero \\ \\ 2. \: \: \: \frac{d( {e}^{ - ct}) }{dt} = - c {e}^{ - ct}$

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