A particle starts from rest with a constant acceleration $$\alpha m/sec^2$$ and after some time it decelerates at a uniform rate of $$\beta 8 m/sec^2$$ till it comes to rest. If the total time taken between two rests positions is t, the maximum velocity acquired by the particle would be

A

$$\frac {\alpha + \beta}{2} t $$

B

$$\frac {\alpha - \beta}{2} t $$

C

$$\left(\frac {\alpha \beta}{\alpha + \beta} \right) t$$

D

$$\left(\frac {\alpha + \beta}{\alpha - \beta} \right) t$$