This paper presents a learning-based approach to consider the effect of unobservable world states in kinodynamic motion planning in order to enable accurate high-speed off-road navigation on unstructured terrain. Existing kinodynamic motion planners either operate in structured and homogeneous environments and thus do not need to explicitly account for terrain-vehicle interaction, or assume a set of discrete terrain classes. However, when operating on unstructured terrain, especially at high speeds, even small variations in the environment will be magnified and cause inaccurate plan execution. In this paper, to capture the complex kinodynamic model and mathematically unknown world state, we learn a kinodynamic planner in a data-driven manner with onboard inertial observations. Our approach is tested on a physical robot in different indoor and outdoor environments, enables fast and accurate off-road navigation, and outperforms environment-independent alternatives, demonstrating 52.4% to 86.9% improvement in terms of plan execution success rate while traveling at high speeds.