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. (a) ` be independt of ` beta`
B. (b) dorpe to zreo when ` alpha = beta`
C. (c ) ` go ondecreasing with tiem
D. (d) ` go on incrasing with time

Answer

D

Explanation

` x= a e^(alpha t) + b d^(beta t)`
` v= (dx)/(dt) =- a alpha e^(alpha t) + b beta e^(beta t)`
As ` t` increases, the value of ` a alpha e^(alpha t)` decreases slowly and the value of ` b, beta e^(beta t)` increases largely. Thes with incresase in ` t, v` will increase.