Given the complex nature of traumatic brain injury (TBI), it has been challenging to identify a single kinematic tolerance threshold that correlates directly with injury risk. In this study, we investigate the role of acceleration, velocity, and jerk on the brain tissue response in an effort to further improve our understanding of the mapping between head kinematics and the risk of brain injury. Prior studies have shown that both acceleration and velocity play a role in brain injury. Furthermore, higher strains and strain rates within the brain tissue are often associated with increased injury risk. To further explore the relationship between kinematic parameters and brain injury, a parametric finite element analysis (FEA) is performed on two-dimensional biofidelic human head models. Angular head motions are studied along the three major anatomical planes (sagittal, coronal, and axial). Acceleration loading profiles with varying magnitudes of peak angular acceleration, velocity, and jerk are applied to the FE models, and the resulting temporal and spatial characteristics of the developed tissue strains and strain rates are studied. Through this systematic approach, we aim to provide further insight into the key kinematic parameters that correlate with increased risk of brain injury.