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. go on decreasing with time
B. be independent of `alpha` and `beta`
C. drop to zero when `alpha=beta`
D. go on increasing with time

Answer

D

Explanation

`x=a e^(-alphat)+b e^(betat)`
`v=(dx)/(dt)=ae^(-alphat)(-alpha)+b e^(betat)(beta)`
`=(-aalpha)/e^(alphat)+b beta e^(betat)`
As t increases, `e^(alphat), e^(betat)` increases
`(aalpha)/e^(alphat)` decreases hence `v` uncreases.