A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate `beta` to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by :

Options

A. `((alpha^(2)-beta^(2))t)/(alpha beta)`
B. `((alpha^(2)+beta^(2))t)/(alphabeta)`
C. `((alpha+beta)t)/(alphabeta)`
D. `(alpha betat)/(alpha+beta)`

Answer

D