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Standard XII

Physics

Instantaneous Velocity

A raindrop fa...

Question

A raindrop falls with velocity v obeying the relation $v = v_{0} (1 - e^{- k t})$ from a large distance where k and $v_{0}$ are constants. Find velocity and acceleration of raindrop at $t \to \infty$ .

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Solution

Given $v = v_{0} (1 - e^{- k t})$ .
Now velocity of the rain drop at $t \to \infty$
$v l i m t ⟶ \infty = v_{0} l i m t ⟶ \infty (1 - e^{- k t}) = v_{0} (1 - 0) = v_{0}$
$e^{- \infty} = 0$
Thus velocity of the raindrop $v = v_{0}$
and acceleration is the rate of change of velocity with respect to time
Thus acceleration $a l i m t ⟶ \infty = \frac{v_{0}}{t} l i m t ⟶ \infty a = 0$

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