A car starts from rest and travels with uniform acceleration $\alpha$, for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of car is $t$, the maximum velocity attained by it is given by :

Question

( A ) $\frac{1}{2} \frac{\alpha \beta}{(\alpha- \beta)}t^2$
( B ) $\frac{\alpha \beta}{(\alpha+ \beta)}t$
( C ) $\frac{\alpha \beta}{(\alpha - \beta)}t$
( D ) $\frac{1}{2} \frac{\alpha \beta}{(\alpha+ \beta)}t^2$