Safe and energy-efficient driving of connected and automated vehicles (CAVs) must be influenced by human-driven vehicles. Thus, to properly evaluate the energy impacts of CAVs in a simulation framework, a human driver model must capture a wide range of real-world driving behaviors corresponding to the surrounding environment. This paper formulates longitudinal human driving as an optimal control problem with a state constraint imposed by the vehicle in front. Deriving analytically optimal solutions by employing optimal control theory can capture longitudinal human driving behaviors with low computational burden, and adding the state constraint can assist with describing car-following features while anticipating behaviors of the vehicle in front. We also use on-road testing data collected by an instrumented vehicle to validate the proposed human driver model for stop scenarios at intersections. Results show that vehicle stopping trajectories of the proposed model are well matched with those of experimental data.