Answer
Event 2 occurs first.
Work Step by Step
Event 2: The rear door reaches the front bumper at $t_{c2} = -1.01\times 10^{-7}~s$
Event 1: The front door reaches the rear bumper at $t_{c1} = 0$, which is after the rear door reached the front bumper.
Therefore, event 2 occurs first.
