Classical mechanics, the branch of physics governing the motion of everyday objects, was formalized by Sir Isaac Newton in his monumental 1687 work "Philosophiae Naturalis Principia Mathematica." Newton's three laws of motion form the bedrock of mechanical physics. The first law (law of inertia) states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship as F equals ma, where force equals mass times acceleration, establishing that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass. The third law states that for every action there is an equal and opposite reaction. Together, these laws explain phenomena from falling apples to orbital mechanics and remain accurate for objects moving well below the speed of light.

Conservation laws represent some of the deepest principles in physics. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. Kinetic energy, the energy of motion expressed as one-half times mass times velocity squared, can convert to potential energy (stored energy due to position or configuration) and back again. A ball thrown upward converts kinetic energy to gravitational potential energy (mgh, where m is mass, g is gravitational acceleration, and h is height) as it rises, and the reverse occurs as it falls. The law of conservation of momentum states that the total momentum of a closed system remains constant, which governs collisions, rocket propulsion, and particle interactions. These conservation laws arise from fundamental symmetries of nature, as demonstrated by Emmy Noether's theorem: conservation of energy corresponds to time symmetry, and conservation of momentum corresponds to spatial symmetry.

The kinematic equations describe motion under constant acceleration and can be derived directly from calculus. Starting with the definition of acceleration as the derivative of velocity with respect to time, integration yields velocity as a function of time: v equals v-naught plus at, where v-naught is initial velocity and a is acceleration. Integrating velocity gives position as a function of time: x equals x-naught plus v-naught times t plus one-half times a times t squared. A third equation relating velocity to displacement without explicit time dependence, v squared equals v-naught squared plus 2a times displacement, is derived by eliminating time between the first two equations. These three equations, along with Newton's laws, enable the analysis of projectile motion, free fall, vehicles accelerating and braking, and countless other physical scenarios. Power, defined as the rate at which work is done or energy is transferred, connects force and energy concepts through the relationship P equals W divided by t, or equivalently P equals F times v, bridging the gap between static force analysis and dynamic energy considerations.