Kinematics Kernels: A Reassessment of Particle Kinematics in Newtonian Mechanics

When a cannonball is shot towards the walls of a fortress, or when the ion drives on a satellite eject gas in order to keep its orbit stable, or, similarly, when we observe the ordinary day-to-day movements of cars, rivers, and other objects, and even the speed of a chemical reaction, we, in fact, are witnessing the effects that physics, or more specifically, kinematics, has on our world. The former, for instance, employs the range formula for projectiles; the satellite, on the other hand, utilizes the concept of velocity to continue being kept afloat in space. Although the latter cases are, respectively, measured in terms of acceleration, distance, and speed (or, depending on the circumstances, in terms of their vectorized counterparts: change in speed, displacement, and velocity); they all, however, do have a shared sense of motion attached to them, which in physics and engineering came to be known as "kinematics." This paper aims to explain the fundamentals of kinematics and clarify the core topics and idioms covered within college-level physics courses, and some of the advanced high school science textbooks, straightforwardly and comprehensively; furthermore, core kinematics concepts and equations will be demonstrated alongside the algebraic proofs of their derived formulae.