Final answer:
In this situation, you should tell the truth and take responsibility for your actions, according to Kant's Deontological Ethics.
Step-by-step explanation:
In this situation, Immanuel Kant's Deontological Ethics would guide you to act based on your moral duty, rather than the consequences of your actions. According to Kant, it is your duty to tell the truth and take responsibility for your actions, even if it means facing criminal charges. Therefore, you should truthfully explain to the tearful woman that you were the one who hit and killed the pedestrian. By doing so, you are acting in accordance with Kant's categorical imperative, which emphasizes the importance of following universal moral principles.