Theory:

From module 4, the basic equations are:

Since a vector consists of both magnitude and direction, if either vary, the vector has a derivative. When an object moves on a curve, it is convenient to define unit vectors which are tangential and radial; that is, they move with the object and are continuously changing directions. Serway shows such vectors on page 88, Figure 4.15a. Since they are unit vectors, their magnitudes are constant (one), but their directions are changing, so they have derivatives. This is too difficult for this course; I have mentioned it only to make you aware that there's a lot more to this topic!

A warning! When using derivatives to find the velocity and acceleration, take the derivatives of the general expressions of the position vector and the velocity. After you've substituted a number for the time (for example), it is invalid to take a derivative!

The examples show you how to do problems for which the Cartesian unit vectors are used.

Example 1: Constant acceleration

Example 2: A Deer Fly

Example 3: Using derivatives