First slide
Instantaneous velocity
Question

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

Moderate
Solution

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

                        = 2e-αt+2eβt

Acceleration is positive so velocity goes on increasing with time

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