The displacement x of a particle varies with time t as x

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The displacement x of a particle varies with time t as x = ae^−αt + be^βt, where a, b, α and β are positive constants. The velocity of the particle will

1. be independent of α and β
2. drop to zero when α = β
3. go on decreasing with time
4. go on increasing with time

Correct Option: D

Given x = ae^–αt + be^βt
Velocity, v = dx/dt = –aαe^–αt + bβe^βt

=	aα	= bβe^βt
	e^αt

i.e., go on increasing with time.