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The displacement x of a particle varies ...

The displacement x of a particle varies with time t as `x = ae^(-alpha t)+be^(beta t)`, where a, b,`alpha` and `beta` are positive constants. The velocity of the particle will

A

Be independent of `alpha and beta `

B

Go on increasing with time

C

Drop to zero when `alpha= beta`

D

Go on decreasing with time

Text Solution

Verified by Experts

The correct Answer is:
B
`x=ae^(-alphat)+ be^(betat)`
`v=(dx)/(dt)=- a prop e^(-alpha t) + . b beta e^(betat)`
`(dv)/(dt) =a alpha^(2) e^(-alpha t) + b beta^(2) e^(beta t)`
`:' (dv)/(dt) gt 0` (Always )
`implies` v is increasing function of t
`implies` option (2) is correct
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