# Day 30: Problem Solvers and Graphical Representations

We’re getting toward the end of CAPM and I’m very impressed with the gains I’ve seen in problem solving ability. These kids are getting pretty good and solving problems using both algebraic and graphical methods. This particular problem was fun because we were able to take a closer look at multiple aspects of the boxed, derived equation. The graph below represents some aspects of it, though it’s a bit hard to tell. The red box is the $v_0 \Delta t$ term, representing the displacement if the object continued at a constant velocity of $v_0$. The $\frac{1}{2}\Delta v\Delta t$ term is the purple shaded region; negative because $\Delta v$ is negative. Thus the displacement, as depicted by the area of the black triangle, is the red rectangle minus the purple triangle. Cool.

We then went on to show that their equation actually simplifies to $\Delta x=\overline{v}\Delta t$, which is then represented by the green rectangle. I love algebraic and graphical connections!

##CAPM

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