Graphing Motion

Imagine a skier going down this mountain. What does his path look like?

Now, what if we graph his motion thinking about time and distance? How will the line look?

At first, you might want to draw a line that curves downward like the skier's path. That feels natural because that's what we see on the mountain.

But on a graph, the line doesn't show the path. It shows how distance changes as time goes on.

Let's think about what that line will look like. On a time and distance graph, the x axis represents time, and the y axis represents distance. We won't mark the tick marks right now because we aren't using real data. This is just about imagining the shape of the line.

And just like with our previous graphs, this one starts at the origin zero zero.

At the very beginning, the skier only moves a little. So as the seconds increase, the distance increases just a little. On the graph, the line begins gently.

Then, the skier hits a big drop. The distance increases quickly. On the graph, the line gets very steep.

After that, the skier slows down. The distance isn't changing as much anymore. On the graph, the line starts to flatten.

Then the skier hits another big drop. Once again, the distance increases quickly. The line gets very steep on the graph.

Finally, the skier slows down and then stops completely. The line starts to flatten until it becomes completely flat straight across.

So the line of the graph reflects motion. A steep line means quick movements. A gentle slope means moving slowly. A flat line means no movement at all.

That's how graphs show how motion changes over time.