Car-following models describe how one vehicle follows the preceding vehicles.ln order to better model and explain car-following dynamics,this paper categorizes the state of a traveling vehicle into three sub-processes:the starting(acceleration)process,the car-folloing process,and the stopping(deceleration)process.The stating process primarily involves vehicle acceleration behavior.The stopping process involves not only car-following behavior but also deceleration behavior.This paper regards both the stopping process and the starting process as spring systems.The car-following dynamics during the starting process and the stopping process is modeled in this paper.The parameters of the proposed models,which are represented in the form of trigonometric functions,possess explicit hysical meaning and definitive ranges.We have calibrated the model of the starting process using data form the Traffic Engineering Handbook and ob-tained reasonable results.Compared with traditional stimulus-response car-following mo Car-following models describe how one of the vehicles follows the preceding vehicles. Order to better model and explain car-following dynamics, this paper of a traveling vehicle into three sub-processes: the starting (acceleration) process, the car- folloing process, and the stopping (deceleration) process. the stopping process involves not only car-following behavior but also deceleration behavior. this paper manner both the stopping process and the starting process as spring systems. The car-following dynamics during the starting process and the stopping process is modeled in this paper. These parameters of the proposed models, which are represented in the form of trigonometric functions, possess explicit hysical meaning and definitive ranges.We have calibrated the model of the starting process using data form the Traffic Engineering Handbook and obturable reasonable results. Compared with traditional stimulus-respon se car-following mo