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Introduction to Kinematics

In classical mechanics, we are ultimately interested with understanding the motion of objects. However, before we can even begin to discuss the causes of such motion (i.e. before we study the dynamics of physical systems), we must first find a way of describing the motion of objects. In other words, we want to develop a mathematical formalism that allows us to represent the position, velocity, and acceleration of moving objects, and to express how these quantities are related to each other in time. This is the project of kinematics.

In the first SparkNote on Kinematics--which deals with one-dimensional motion--we introduce position, velocity, and acceleration functions to keep track of an object's position along a single spatial direction as it changes in time. In the second SparkNote, we will expand this analysis to two and three dimensions by considering vector-valued versions of our original position, velocity, and acceleration functions. At the end of each SparkNote, we will use our newly developed formalism to solve problems of motion with constant acceleration. This includes commonplace phenomena such as free fall and projectile motion.