This paper introduces RACER, the Rational Artificial Intelligence Car-following model Enhanced by Reality, a cutting-edge deep learning car-following model, which satisfies partial derivative constraints that are necessary to maintain physical feasibility, designed to predict Adaptive Cruise Control (ACC) driving behavior. Unlike conventional car-following models, RACER effectively integrates Rational Driving Constraints (RDC), crucial tenets of actual driving, resulting in strikingly accurate and realistic predictions. Notably, it adherence to the RDC, registering zero violations, in stark contrast to other models. This study incorporates physical constraints within AI models, especially for obeying rational behaviors in transportation. The versatility of the proposed model, including its potential to incorporate additional derivative constraints and broader architectural applications, enhances its appeal and broadens its impact within the scientific community.