Lesson 8: Graphs

Graphing displacement, velocity, and acceleration stuff can be one of the harder things for students to figure out in this unit.

Graphing Rules

Graphs you draw must have the following five basic characteristics:

1. A Title

When you do a lab, you are usually changing or letting something change at a regular rate, and watching for changes in something else. What you are changing is the independent or manipulated variable, drawn on the x-axis. The one that you're watching for changes in is called the dependent or responding variable, drawn on the y-axis.

2. Labelled Axis

3. A Well Chosen Scale

4. The Correct Data Plotted

5. A Best Fit Line

This step is sometimes optional (as you’ll see on the graphs we will be studying here!).

Displacement - Time (d-t) Graphs

Although this type of graph is based on the most basic things we need to know about the motion of an object (position and time), it is also one of the most complex.

For the example graph shown below, imagine that you are running in a marathon, and we have decided to graph your movement.

Zero to 90s

Look at how you are running in those first 90 seconds.

90s to 150s

Yikes! You ran too fast at the start and now you’re out of breath!

150s to 240s

You must have started running forward again, since a positively sloped line means a positive velocity.

240s to 300s

In this section the line slopes down, which means it has a negative slope.

300s to 360s

Again, we have a horizontal line. You must be stopped.

360s to 510s

You know that you have only one chance to still win the race… run as fast as you can!

Here’s how I used to remember if it was positive or negative acceleration on a d-t graph.

Velocity-Time (v-t) Graphs

You need to remember that the rules you learned above for d-t graphs do not apply to v-t graphs.

Zero to 90s

Remember that in the first 90 seconds you were running at a positive constant velocity.

90s to 150s

This is the section of time when you stopped because you are out of breath.

150 to 240 seconds

You are running forward again.

240 to 300 seconds

This is when you are running back to the check point.

300 to 360 seconds (jump back to v-t graph)

Again, we have a horizontal line at zero. You must be stopped.

360 to 510 seconds (jump back to v-t graph)

This is the section when you run faster and faster.

There is one other trick you need to know about v-t graphs.

Acceleration time Graphs

Acceleration-time graphs are probably the most boring and least often used of the three graphs.

The First 360 seconds…

Nothing, nada, zip. For most of the race you were not accelerating.

360 to the end…

We know you were accelerating during this time.