A Flat Line

Rate of change

Let’s start with a very easy scenario to get ourselves settled and ready to go.

Imagine that car again, but it’s cruising at a constant speed of 30 mph. Not faster, not slower, just a constant 30 mph.

Here’s a table showing the speed at various points in time, measured every half minute:

Time (mins)	Speed (mph)
0.0	30
0.5	30
1.0	30
1.5	30
2.0	30
2.5	30
3.0	30

The following graph visualizes this speed at those points in time:

We can see that the speed doesn’t change over time, and that’s why it is a straight horizontal line. It doesn’t go up (faster) or down (slower), it stays at 30 mph.

The mathematical expression for the speed, which we’ll call $s$, is:

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