Previous studies have described vehicle acceleration profiles in non-car-following scenarios; however, the underlying mechanisms governing these profiles remain incompletely understood. This study aims to enhance the understanding of these mechanisms by proposing an improved model based on an optimal control problem with two bounded conditions (OCP2B), segmenting vehicle acceleration curves into three distinct phases. Specifically, the proposed model imposes constraints on acceleration through maximum jerk and maximum acceleration functions, thereby capturing essential dynamics previously unexplained by conventional models. Our key contributions include establishing a comprehensive analytical framework for accurately describing vehicle acceleration profiles and elucidating critical characteristics overlooked in the prior literature. Our findings demonstrate that incorporating human-centric considerations, such as driving comfort, significantly enhances the model’s practical applicability. Moreover, the proposed approach provides crucial insights for designing autonomous vehicle (CAV) trajectories consistent with human driving behaviors and effectively predicts the movements of human-driven vehicles (HVs), thus facilitating smoother interactions and potentially reducing conflicts between CAVs and HVs.