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.