# Kinematics Graphs

On a quiz from October of the past year.

In the comments, let’s get started with some practice picking our way into the student brain.

- What was the student thinking? How did he or she decide to make these particular marks on the paper?
- What question or problem would you pose next to help the student make the next step toward understanding?

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In going from position to velocity, it looks like the student is thinking something along the lines of slope of position graph = velocity, but they’re having some trouble in a few places, like in the second part of set 2, where they should be seeing that that slope is zero, they can’t quite see the moments of constant slope paired next to moments where velocity is changing. They have trouble seeing that in set 3 the object is starting from rest, and somehow see the object as speeding up even more after the dashed line. Maybe that’s time to some sort of prim “when the position is going up the most, it must be speeding up.

I would address this by asking the person to draw two vertical lines in set 2 after the dotted line and compare what happens to the position of the object. Then the student would see that it isn’t changing, and that the velocity must be zero.

For set 3, I might ask them to try to extend the graph to before t=0, and again, consider two points and take notice of the idea that the position isn’t changing.

For the translation from velocity to acceleration, i’m tempted to think that the student is sort of taking a stab in the dark and just drawing something, but they generally seem to have some sort of “when velocity is big acceleration is big” idea going on.

To work on this, I might take the acceleration graph and have the student write me a story of just what the acceleration is doing as they drew it. (set1: the car’s acceleration is large and positive, and then the acceleration is a bit smaller but still positive). Then I’d have explain to me what acceleration is, and try to draw a velocity graph for the acceleration graph they drew. Hopefully, they’d see that if the car is accelerating, there’s no way the velocity can be constant.

You’re also right about how awesome these mistakes blogs are. It took me a decent bit of time starting at these mistakes to come up with anything intelligible to say, and I’m still not sure I’ve got the thing that is really going to help this kid.

It looks like this student has trouble separating slope from value in going from one graph to the next.

Is it possible for an object in a negative position to have a positive velocity? Show me an example.