Today when position graphs, one student asked how the graph would change if the origin was different. He thought the position graphs would no longer be linear. I had students talk in groups about what the graph would look like if the origin was between A and B’s starting positions. I had a student come draw her new graph on the board. Instead, she just drew shifted axes on the same graph – smart! 

(And after further probing, I learned that the student who had the question was actually thinking about 2-dimensional space, and what if the origin was not on path that A and B were traveling. good question!)

Later, students were concerned about making a velocity graph from a position graph that starts at time t=0. Some students really wanted to use closed circles or open circles for the endpoints of the lines. They thought if the position graph endpoint is a closed circle, than the velocity graph would have to start with an open circle, since you can’t actually find the slope of the position graph at t=0. Idea on how to respond to this other than saying there’s things math teachers care about that physicists don’t? Maybe that the slope immediately after t=0 is essentially the same as the slope at t=0?

Later in class, I was showing how you could solve the position equation for velocity, and you got back to the slope of the position graph. There was an audible gasp from multiple students!