Th displacement x of a particle varies with time t as x = ae-αt+beβt, where a, b, α and β are positive constants. The velocity of the particle will
go on decreasing with time
be independent of α and β
drop to zero when α = β
go on increasing with time
We are given
x = ae-αt+beβt
Velocity v = dxdt = ddt(ae-αt+beβt)
= a.e-αt(-α)+beβt.β
= -aαe-αt+bβeβt
Acceleration = -aαe-αt(-α) +bβeβt.β
= aα2e-αt+bβ2eβt
Acceleration is positive so velocity goes on increasing with time