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 given

$x = {ae}^{- α t} + {be}^{βt}$

Velocity v = $\frac{dx}{dt} = \frac{d}{dt} ({ae}^{- αt} + {be}^{βt})$

= $a . e^{- αt} (- α) + {be}^{βt} . β$

= $- {aαe}^{- αt} + {bβe}^{βt}$

Acceleration = $- {aαe}^{- αt} (- α) + {bβe}^{βt} . β$

= ${aα}^{2} e^{- αt} + {bβ}^{2} e^{βt}$

Acceleration is positive so velocity goes on increasing with time

Th 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