# Day 8: “Aha” moments with kinematics graphs

Kinematics is clicking into place for the Mechanics students. We wrapped up the TIPERs problems in our packet (including whiteboarding), and we’re ready to add in the quantitative side by using the graphs to solve problems.

For this problem, there was a lively discussion about tangent lines (ARE THEY REAL OR MADE UP???), the intermediate value theorem, and whether you could say two things had the same speed if they didn’t both go at that same speed for any length of time*. The velocity-time graphs that they tucked into the bottom right corner of their whiteboard turned out to be the crowd-pleaser when it came to being convinced about the speeds being the same at a point in time.

After some working and some whiteboard discussions, we took our second quiz. They aren’t perfect yet (of course), but they are clearly in a better place than last week, and we can definitely move on to Unbalanced Forces (and “for real” physics) next week. I’m excited!

Here’s a piece that I loved on one student’s quiz.

She writes:

I believe this is correct, because if her acceleration is negative, the slope of the line on the velocity v. time graph is negative, too, [arrow to v-t graph she drew at top right] meaning that she was slowing down. However, one thing that I am confused by is what if the velocity graph looked like this (LOOK at graph on left top). [arrow to v-t graph she drew at top left] This graph also shows her slowing down, with a line that has a POSITIVE slope (just a negative direction). HOW DO I KNOW WHICH ONE TO FOLLOW?

I love everything about it. She starts with all true statements that connect the acceleration to the slope on the velocity graph, stops in the idea that negative acceleration means slowing down, but continues right past it into finding a counter-example to that idea. She lays out her thinking carefully. She isn’t afraid to say that she’s confused or to ask me questions on the assessment. Love, love, love. I wrote her a couple of notes back (although most of it was cut off in this photo).

*Days like today make you really wish your school could have a double class of physics and calculus for the kids who are into that sort of thing.