The branch of Physics which deal with the motion of objects while taking into consideration the cause of motion is:

Dynamics is the branch of physics and a sub branch of Mechanics. Dynamics is concerned with the motion of material objects and also concerns with the cause of motion. It deals with the factors that affect motion such as force, mass, momentum and energy.

Whereas, Statics deals with objects at rest and Kinematics deals with objects in motion without considering the cause of motion.