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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 $t = 0$ .

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Solution

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

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A raindrop falls with velocity v obeying the relation v=v0(1−e−kt) from a large distance where k and v0 are constants. Find velocity and acceleration of raindrop at t=0.

Given v=v0(1−e−kt).Now velocity of the rain drop at t→0vlimt⟶0=v0limt⟶0(1−e−kt)=v0(1−1)=0e0=1Thus velocity of the raindrop v=v0and acceleration is the rate of change of velocity with respect to time Thus acceleration alimt⟶0=0tlimt⟶0a=0

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 $t = 0$ .