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

Answer

A