The displacement x of a particle varies with time t as x=a e^ -α t...

Given, $x=a e^{-\alpha t}+b e^{\beta t}$ We know that, velocity, $v=\frac{d x}{d t}$$\begin{aligned} & \quad \frac{d}{d t}\left(a e^{-\alpha t}+b e^{\beta t}\right) \\ &=-a \alpha e^{-\alpha t}+b \beta e^{\beta t} \\ &= A+B\end{aligned}$$$where,$A=-a \alpha e^{-\alpha t}, B=b \beta e^{\beta t}$The value of term$A=-a \alpha e^{-\alpha t}$increases and of term$B=b \beta e^{-\beta t}$ increases with time. As a result, velocity goes on increasing with time.