Highway driving invariably combines high speeds with the need to interact closely with other drivers. Prediction methods enable autonomous vehicles (AVs) to anticipate drivers' future trajectories and plan accordingly. Kinematic methods for prediction have traditionally ignored the presence of other drivers, or made predictions only for a limited set of scenarios. Data-driven approaches fill this gap by learning from large datasets to predict trajectories in general scenarios. While they achieve high accuracy, they also lose the interpretability and tools for model validation enjoyed by kinematic methods. This letter proposes a novel kinematic model to describe car-following and lane change behavior, and extends it to predict trajectories in general scenarios. Experiments on highway datasets under varied sensing conditions demonstrate that the proposed method outperforms state-of-the-art methods.