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 :

The velocity of the particle can be found by taking the derivative of the displacement with respect to time: v = dx/dt = -αae^(-αt) + βbe^(βt). Given that α and β are positive constants, the term -αae^(-αt) will decrease with time (since e^(-αt) decreases as t increases), and the term βbe^(βt) will increase with time (since e^(βt) increases as t increases). The overall behavior of the velocity depends on the relative magnitudes of these two terms. However, since both α and β are positive, and assuming a and b are also positive, the increasing term (βbe^(βt)) will eventually dominate the decreasing term (-αae^(-αt)) as time progresses, causing the velocity to increase with time.