Even though we live in a three-dimensional world, it is useful to understand the motion of objects in just one dimension, since many physical problems can be reduced to this simpler case. For example, the motion of a falling object is in essence a one-dimensional problem: the object moves in only one direction (down). We will also find (in the next Sparknote) that once we have the formalism for motion in one dimension, it will be easy to generalize our equations to two and three dimensions by replacing our scalar-valued functions for position, velocity, and acceleration with vector-valued ones.
This SparkNote will be divided into three parts. In the first part we will discuss examples of position functions, and then go on to show their relationship to velocity and acceleration in the second part. The third part will consist of studying motion with constant acceleration, including applications to everyday physical phenomena such as the motion of objects in free fall.