During our PLC chat this week, we talked at one point about how long it takes for students to become completely consistent in drawing motion graphs. My experience has been that students become confident relatively quickly in drawing the velocity-vs-time graphs (having switched their brain into thinking through v-t graphs), but still sometimes struggle to draw the matching position-vs-time shapes. I shared a quick tool that I sometimes give to students (more in a one-on-one setting than telling the whole class at once, usually) when they are really having a tough time drawing the curves. I thought I would post it here, too, for reference.

Sometimes it is easier to choose from a menu than to create the shape on the spot. So, if you’re having trouble deciding the shape of your x-t graph, draw a circle and divide it into four pieces.

These sections of the circle are the four possible x-t parabola shapes. Now you can identify the matching graph instead of generating it.

I discourage them from trying to use this as a memorization tool. Instead, I tell them to use it as something they can quickly sketch and then use as a thinking tool while trying to draw a graph. They can identify which of the four shapes is the one that matches their verbal description of their velocity-time graph and draw that shape on their position-time graph.

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## About Kelly O'Shea

I teach high school kids physics at an independent day school in NYC. Less homework, more thinking.

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I like it! Hope I can remember it next fall when the topic returns.

It is hard! I love your circle idea!

Can I share a suggestion, too? Concave up graphs look like happy faces, concave down graphs look like sad faces. If you split the happy and sad faces in half down the middle you get the two possibilities for each.

Upwards sloping velocity lines create happy faces, downward sloping velocity lines create sad faces. Which half you use corresponds to whether the velocity is positive or negative.

I am a college student learning physics. I was confused by this concept until it finally clicked. Many of my friends are still struggling with this concept however. I think this is an awesome way to not just memorize it but to understand it. Is there a way to do this for acceleration vs time? In college there is so much to “memorize” but this post helps me and others to understand the concept.

Acceleration is the slope on the velocity-vs-time graph. So the easiest way to make sure you’re getting the acceleration graph correct is to look at the velocity graph. Describe the slope (is it positive, negative, or zero? is it constant or changing?) and those will be the descriptions of the acceleration value (constant positive slope on v-t means constant positive acceleration, etc). Hope that helps! :)