This text is meant to accompany class discussions. It is not everything there is to know about uniform circular motion. It is meant as a prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)
Here's the question. The motion of a vehicle is not steady. It varies according to the graph below. The question is how do you find the slope at a point in time on a curved graph. For example: What is the slope at 15 seconds on the curve below.