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# Motion Maps

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UNIT II READING MOTION MAPS A motion map represents the position velocity and acceleration of an object at various clock readings At this stage of the class you will be representing position and velocity only Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity where each image revealed the position of the car at one second intervals This is the motion map that represents the car We model the position of the object with a small point At each position the object s velocity is represented by a vector If the car were traveling at greater velocity the strobe photo might look like this The corresponding motion map has the points spaced farther apart and the velocity vectors are longer implying that the car is moving faster If the car were moving to the left at constant velocity the photo and motion map might look like this More complicated motion can be represented as well Here an object moves to the right at constant velocity stops and remains in place for two seconds then moves to the left at a slower constant velocity Modeling Workshop Project 2002 1 Unit II Reading Motion Maps v2 0 Consider the interpretation of the motion map below At time t 0 cyclist A starts moving to the right at constant velocity at some position to the right of the origin Cyclist B starts at the origin and travels to the right at a constant though greater velocity At t 3 s B overtakes A i e both have the same position but B is moving faster A graphical representation of the behavior of cyclists A and B would like this You could also represent the behavior algebraically as follows x vAt x0 for A x vBt for B where vB vA Throughout this semester you will be representing the behavior of objects in motion in multiple ways diagramatically motion maps graphically and algebraically Modeling Workshop Project 2002 2 Unit II Reading Motion Maps v2 0

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