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.)
The velocity of the car on the the previous page is 1 m/s. The velocity is constant. At the start, (0 seconds,) the velocity is 1 m/s; at 1 s it is 1 m/s; at 2 seconds it is still 1 m/s; at 3 seconds it remains 1 m/s; at 4 seconds it is still 1 m/s and at 5 seconds it is also 1 m/s. A graph of the look like the one below.
Look at the slope on the previous graph of position vs time.
The slope on the position vs time graph equals the velocity.
Let's change the situation. Instead of the car traveling at a constant velocity suppose its velocity changes by 1 m/s every second. This is a constant acceleration of 1 m/s2. After 1 second, it would be traveling at 2 m/s; after 2 seconds, it would be traveling at 3 m/s; after 3 seconds it would be traveling at 4 m/s; at 4 seconds the velocity would be 5 m/s, and after 5 seconds it would be traveling at 6 m/s. The graph of the car's velocity would look like the one below.