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Figure 2.1: Positions = +3 m and = –2 m, where the + and – signs indicate the direction. Figure 2.2 : The displacement is –5 m when moving from position to position .
Introduction to Position-Time Graphs Position-Time Graphs tell you where an object is located over a period of time. The slope of the graph tells you how fast the object is moving. The sign of the slope indicates direction of motion. What would a graph look like if an object is… Moving away from 0 meters Stopped Moving towards 0 meters.
Distance in Graphs This lecture introduces the notion of a weighted graph and explains how some choices of weights permit us to define a notion of distance in a graph. Reading: The material in this lecture comes from Chapter 3 of Dieter Jungnickel (2013), Graphs, Networks and Algorithms, 4th edition, which is (available online via SpringerLink.
Answer: 1) 135 km, 85km forward 2) 0 m, 6 m • Distance ( ): the separation between two points. Ex, the length of an object. Usually measures in _____. No _____ needed ex) • Displacement ( or ): A measure of the change in position. Needs _____ Δd = final position – initial position.
If the shortest path distance between two vertices i,j ∈V is d ij, then stress majorization will attempt to place these two vertices at distance d ij apart in the layout. To accomplish this, stress majorization uses an iterative optimization process to find a global minimum of the stress function shown in Equation 5.
The distance between two vertices in a graph is a simple but surprisingly useful notion. It has led to the definition of several graph parameters such as the diameter, the radius, the average distance and the metric dimension.
Examples: Find the distance between the points (-3,7) and (4,10). Determine whether the triangle formed by points A=(-2,2), B=(2,-1), and C=(5,4) is a right triangle. Find the midpoint of the line segment joining the points P1=(6,-3) and P2=(4,2).
