Displacement of particle changes with respect to time according to equation x =ae ^(-alpha t) + be ^(betat)where a, b, a and Bare positive constants, then velocity of particle is ......

Displacement of particle changes with respect to time according to equ

1.	Displacement of particle changes with respect to time according to equation x =ae ^(-alpha t) + be ^(betat)where a, b, a and Bare positive constants, then velocity of particle is ......
Answer» indipendent of `alpha and beta` will be zero if `alpha = beta.` will increase with repsect to time. will increase with respect to time. SOLUTION :`x = AE ^(-alphat ) + be ^(beta t )` `therefore (DX)/(dt) =a (e ^(- alpha t )) (-alpha ) + B ( e ^(beta r )) (beta)` `therefore v =- aalpha e ^(- alpha t ) + b beta e ^(beta t )` `= b beta e ^(beta t )- a alpha e ^(- alpha t)` `= b beta e ^(beta t) - (a alpha)/(e ^(alpha t))` THUS, `(a alpha )/(e ^(alpha t))` will increase with increase of t and velocity will increase.