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Simulation Software Integration Connect Velocity and Acceleration to Mathematical Models

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Graphing Motion Introduce Linear Functions Unit with Linear Regression activity collecting walking distance data. Review this with students using Moving Man Applet with velocity only. http://phet.colorado.edu/en/simu lation/moving-man

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Student Review What equation can you write to model a man starting a 0 with a velocity of 2m/s? – Let’s use x to represent time and y to represent his position. – Based on this equation, how long should it take for him to hit the wall? – Verify this with the simulation software. What is the equation if he is at 6 feet and walks at speed of.25m/s? – How long should it take him to hit the wall? – Were you correct? What if he is at -4 feet and walks at a speed of.25m/s. Create your own example. – How long do you expect it to take him? Were you correct?

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Add Acceleration So far we have been walking at a constant rate with a straight line graph or linear function. What do you predict the line will look like if the walker accelerates as he is walking. (Gets consistently faster) Lets try, position the walker at -10, with velocity of 1 m/s and acceleration of 1m/s2. Review the playback. What was happening to his speed during over time? What did the graph of velocity vs time look line? How did his speed increase? After 2 seconds, what was his speed? Is the velocity curve linear?

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Compare Distance over time Linear and with Acceleration Now look at the graph of distance vs time. – Is this still linear? – Can you use your equation to calculate distance like you did before? – Why or Why not? Looking for students to recognize that the since the rate is changing that the line is no longer linear.

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