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

The displacement `x` of a particle varies with time `t` as `x = ae^(-a

1.	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.A. go on decreasing with timeB. be independent of `alpha` and `beta`C. drop to zero when `alpha=beta`D. go on increasing with time
Answer» Correct Answer - D `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.

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