The lack of explainability in AI-driven autonomous vehicles (AVs) remains a key barrier to user trust and adoption. Current AV systems provide minimal transparency, leading to algorithm aversion and safety concerns. This study examines how AI explainability—focusing on benevolence (user-centered decision-making) and competence (technical proficiency)—influences affective and cognitive trust, shaping perceived safety and adoption intention. Through an online experiment and a lab-based study, we assess the impact of AI transparency under varying driving conditions and cognitive load. The findings will offer insights into designing explainable AI (XAI) systems that enhance user trust and adoption, supporting safer and more transparent AV technology.