\(\bar{x} = ae^{-\alpha t} + be^{\beta t}\)

Velocity \(\mathbf{v} = \frac{dx}{dt} = \frac{d}{dt} \left( ae^{-\alpha t} + be^{\beta t} \right)\)

\(= a.e^{-\alpha t} \left(-\alpha\right) + b e^{\beta t} \left(\beta\right)\) \(= - a \alpha e^{-\alpha t} + b \beta e^{\beta t}\)

Acceleration \(= -a \alpha e^{-\alpha t} \left(-\alpha \right) + b \beta e^{\beta t} \cdot \beta\)

\(= a \alpha^{2} e^{-\alpha t} + b \beta^{2} e^{-\beta t}\)

Acceleration is positive so velocity goes on increasing with time.