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

We are givenx = ae-αt+beβtVelocity   v = dxdt = ddt(ae-αt+beβt)                     = a.e-αt(-α)+beβt.β                    = -aαe-αt+bβeβtAcceleration = -aαe-αt(-α) +bβeβt.β                        = aα2e-αt+bβ2eβtAcceleration is positive so velocity goes on increasing with time