Which of the following will be called as the study of motion of the body with respect to the time, displacement, velocity, and speed of movement either in a straight line or in a rotary direction?

The correct option is Kinematics.

To understand why this is the correct answer, let us break down the study of mechanics and its various branches:
1. Mechanics is the branch of physics that deals with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
2. Mechanics is broadly divided into Statics (the study of bodies at rest or moving with constant velocity under equilibrium) and Dynamics (the study of bodies in motion).
3. Dynamics is further subdivided into two branches:
    • Kinematics: This branch describes the motion of points, bodies, and systems of bodies without considering the forces that cause the motion. It focuses purely on the parameters of motion such as displacement, velocity, acceleration, speed, and time. The motion can be linear (in a straight line) or angular/rotary.
    • Kinetics: This branch studies the relation between the action of forces on bodies and the resulting motion, meaning it focuses on the forces and masses that cause the motion.

Since the question asks for the study of motion of a body with respect to time, displacement, velocity, and speed (which are description-of-motion parameters) without mentioning the forces causing the motion, it corresponds directly to the definition of Kinematics.