Question

The displacement x of a particle varies with time according to the relation x=a/b(1-e^-bt).then select the false statements..
A)at t=1/b the displacement of the particle is nearly 2/3(a/b)
B)the velocity & acceleration of the particle at t=0 are a and -ab respectively
C)the particle cannot go beyond x=a/b
D)the particle will not come back to its starting point at t--infinity

Answer 1

Answer:

Option (D) is incorrect as we can see that rest all options satisfying the conditions

Explanation:

As we know that displacement is given as

$x = \frac{a}{b}(1 - e^{-bt})$

so we will have

A) at t = 1/b we have

$x = \frac{a}{b}(1 - e^{-1})$

which is nearly equal to

$x = \frac{a}{b}(1 - \frac{1}{3}) = \frac{2a}{3b}$

B)for velocity of the particle we have

$v = \frac{dx}{dt}$

$v = \frac{a}{b}(be^{-bt})$

at t = 0

$v = a$

now for acceleration

$a = \frac{dv}{dt}$

$a = -abe^{-bt}$

at t = 0

$a = - ab$

C) for maximum value of displacement we can say that

$t = infinite$

$x = \frac{a}{b}$

so it can not go beyond a/b

#Learn

Topic : Kinematics

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