PPT-Graphs of Motion: P-T, V-T, and A-T

September 20 2016 What do we already know about graphing motion We know how to draw and interpret position vs time PT graphs Straight lines Positive slope Negative slope Zero slope . Describing the motion of an object is occasionally hard to do with words. Sometimes . graphs. help make motion easier to picture and therefore understand.. Remember:. Motion. is a change in position measured by distance and time.. Masaru . Kamada. Tokyo . University of . Science. Graph Theory Conference. i. n honor of Yoshimi . Egawa. on the occasion his 60. th. birthday. September 10-14, 2013. In this talk, all graphs are finite, undirected and allowed multiple edges without loops.. Kinematics Terminology. Scalar vs. Vector. Scalar: . quantities that have only a size, but no direction. i. e. : . distance, speed. Vector: . quantities that have a size and direction. ie. : . displacement, velocity. Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . Graphs.  . Graphs . capture . much more detail than numerical summaries, so very useful for learning about data and communicating its features.. At the same time, graphical interpretation isn’t standard in the way that numerical summaries are, and our eyes can fool us.. Daniel A. Spielman. Yale University. AMS Josiah Willard Gibbs Lecture. January . 6. , 2016 . From Applied to Pure Mathematics. Algebraic and Spectral Graph Theory. . . Sparsification. :. a. pproximating graphs by graphs with fewer edges. Use the units of mass, length, and time.. Define displacement, velocity, and acceleration.. Use the units of displacement, velocity, and acceleration.. Measure velocity and acceleration.. Use distance-time and velocity-time graphs.. Thanks to Mr. Hammond @ . www.mrhammond.org/math/mathlessons/7-8.ppt. Review. We have been looking at many different ways to present data. . Now let’s see how people can use these charts and graphs to mislead you.. Physics. How to interpret a . Position. vs. time Graph. Low on the graph. .. High on the graph. .. Slopes uphill.. Slopes downhill.. 0. x. t. Near. Far. Away. Toward. How to interpret a . Position. vs. time Graph. The vertical scale is too big or too small, or skips numbers, or doesn’t start at zero.. The graph isn’t labeled properly.. Data is left out.. But some real life misleading graphs go above and beyond the classic types. Some are intended to mislead, others are intended to shock. And in some cases, well-meaning individuals just got it all plain wrong. These are some of my favorite recent-history misleading graphs from real life.. Planar graphs. 2. Planar graphs. Can be drawn on the plane without crossings. Plane graph: planar graph, given together with an embedding in the plane. Many applications…. Questions:. Testing if a graph is planar. (. pg. 30-55). Do Now. Why is it important to describe and analyze motion. ?. How fast?. How far?. Slowing/Speeding?. Rest/Constant velocity. What . are some of the different types of motion. ?. Translational – motion along a straight line. Sinusoidal Graphs. Sinusoidal Graphs. Periodic Function. Graphs of sine and cosine functions.. Functions whose graphs have a repeating pattern.. Period. The horizontal length of each cycle in a periodic graph.. Position. vs. time Graph. Low on the graph. .. High on the graph. .. Slopes uphill.. Slopes downhill.. 0. x. t. Near. Far. Away. Toward. How to interpret a . Position. vs. time Graph. Steep slope..