Velocity $v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}(a{e^{ - \alpha t}} + b{e^{\beta t}})$

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

Acceleration $ = - a\alpha {e^{ - \alpha t}}( - \alpha ) + b\beta {e^{bt}}.\beta $

$ = a{\alpha ^2}\,{e^{ - \alpha t}} + b{\beta ^2}{e^{\beta \,t}}$

Acceleration is positive so velocity goes on increasing with time.