Alphymus

You are driving a car that has a maximum acceleration of $a$. The magnitude of the maximum deceleration is also $a$. What is the maximum distance that you can travel in time $T$, assuming that you begin and end at rest?

(A) $2aT^2$
(B) $aT^2$
(C) $aT^2 / 2$
(D) $aT^2 / 4$
(E) $aT^2 / 8$