You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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 $t = 0$ .

Open in App

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 $a l i m t ⟶ 0 = \frac{0}{t} l i m t ⟶ 0 a = 0$

Suggest Corrections

Similar questions

Q. 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

The acceleration of a particle, starting from rest, varies with time according to the relation a = Kt + C, where K and C are constants of motion. The velocity ‘V’ of the particle after a time ‘t’ will be

Q. The relation between the time

t

and distance '

x

' is given by

t = p x^{2} + q x

, where

p

and

q

are constants. The relation between velocity

v

and acceleration

f

Q. A point moves rectilinearly with deceleration which depends on the velocity

v

of the particle as

a = k \sqrt{v}

, where

k

is a positive constant. At the initial moment the velocity of the point is equal to

v_{0}

. What distance will it cover before it stops ?

Q. The deceleration experienced by a block under a force is given by

a = - b v

; where a

=

acceleration, v

=

velocity'; b

=

constant. If

^{'} v_{0}^{'}

is magnitude of velocity at

t = 0

, find velocity after time 't'.

Join BYJU'S Learning Program

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 $t = 0$ .