Here are the most important screenshots from this week:

PhyFl18SS1.7.1 sheet 1.7.5 ant crawling around basketball.

PhyFl18SS1.7.2 sheet 1.7.6 A little circular motion GSUA

PhyFl18SS1.7.3 Sheet 1.7.7 You can think about any type of linear motion on the surface of the earth as if it were circular motion since the world is a big ball. just like the ant crawling around the basketball.

PhyFl18SS1.7.4 sheet 1.9.(the top of the back) From our pinwheels in the courtyard.

PhyFl18SS1.7.5 Sheet 1.9.5 The birth of the cosine function. That’s all sines and cosines are. They are circular motion spread out over time. Actually, they are one dimension of that circular motion spread out over time. In this case here, the vertical component of the circular motion is laid out over time. See the animation on my website. If you can get this one thing down it will make physics and math so much easier for you.

PhyFl18SS1.7.6 1st hour trippin run.

PhyFl18SS1.7.7 1st hour x vs. t piecewise function from the trippen run showing the 5 different interval velocities and the overall average velocity

PhyFl18SS1.7.8 2nd hour trippin run

PhyFl18SS1.7.9 2nd hour x vs. t piecewise function from the trippen run showing the 5 different interval velocities and the overall average velocity.

PhyFl18SS1.7.10 3rd hour trippin run

PhyFl18SS1.7.11 3rd hour x vs. t piecewise function from the trippen run showing the 5 different interval velocities and the overall average velocity

PhyFl18SS1.7.12 6th hour trippin run

PhyFl18SS1.7.13 6th hour x vs. t piecewise function from the trippen run showing the 5 different interval velocities and the overall average velocity

PhyFl18SS1.7.14 7th hour trippin run

PhyFl18SS1.7.15 7th hour x vs. t piecewise function from the trippen run showing the 5 different interval velocities and the overall average velocity

PhyFl18SS1.7.16 the old baseball example of distance vs. displacement. For example: If I hit a double, my distance would be 180 ft, but my displacement would be 127 ft.

PhyFl18SS1.7.17 An example of a weighted average a teacher might do for grades.

PhyFl18SS1.7.18 This is a new type of graph for us. It is called a slope graph. It is also called a derivative graph. In this case it is a velocity vs. time graph. It shows what the five interval velocities of the trippin run. This is a VERY important screenshot. It is where we are going next and it is the beginning of your journey into graphical calculus. This graph is the derivative part of the x vs. t graph. Together they form red duets. An example of a weighted average for our step function can be seen by comparing the darker flat segment compared to the 5 orange segments. The darker segment is the weighted average of the 5 orange segments.