The branch of physics that deals with the motion of objects while considering the cause of motion is
Dynamics
Explanation for incorrect option:-
B. The branch of physics that defines motion with respect to space and time, ignoring the cause of that motion, is known as kinematics.
C. Statics, in physics, is the subdivision of mechanics that is concerned with the forces that act on bodies at rest under equilibrium conditions.
Explanation for correct option:-
A.
Hence, option A is correct. The branch of physics that deals with the motion of objects while considering the cause of motion is Dynamics.