Which branch of mechanics deals with the geometry of the motion of objects (including displacement, velocity, acceleration)?

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Describing motion in space and time is what this branch does. It focuses on the geometry of motion: where an object is (displacement), how fast it’s moving and in what direction (velocity), and how its speed or direction changes (acceleration). This description of motion is separate from why motion happens, which is the realm of kinetics (the study of forces and their effects). Biomechanics applies these principles to biological systems, but the specific study of the geometry of motion itself is kinematics. Mechanics as a whole covers both the description (kinematics) and the causes (kinetics) of motion, but the geometry-focused aspect is kinematics.