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

Options

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

Answer

B

Explanation

`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