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.
