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# Gallery Presentation2[1]

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• The Distance, The Displacement and the Position --- By Matthew Symonds
• Let’s look at another example. Here we see Superman doin’ what he does best. What is it that he does best, you ask? He flies frantically around the planet, over and over again. You see, the story goes like this: Superman sees a catastrophe, and it’s too late to deal with it. The only was Superman can save the world is if he goes back in time. Now the idiot thinks that using his motion to change the spin of the earth on its axis will somehow make time go backwards, but let’s let Superman do his thing and see what happens.
• Now you can see a graph of what superman was doing. He was making a circular path around the planet, so his displacement went up and down like the wavy red graph. Depending on where we put the origin, Superman’s position is the purple graph – maybe a little to the left or a little to the right. His distance though, just keeps on going up and up. Even if he comes back to Metropolis over and over again his distance will continue to increase. Keep in mind, however, that the distance and displacement in this example are only his conceptual distance and displacement. You can’t really graph distance and displacement because they’re two dimensional values, aka vectors. They have a magnitude AND a direction. This graph is just convenient to think about.
• ### Gallery Presentation2[1]

1. 1. By Matthew Symonds By Matthew Symonds
2. 2. Distance
3. 3. “ I have traveled a very great distance, but now I’m BACK.”
4. 5. Distance = 3m + 1m = 4m
5. 6. Distance = (3m + 1m)2 = 8m
6. 7. Distance <ul><li>Distance is a scalar </li></ul><ul><li>Scalars are magnitude only </li></ul><ul><li>Total distance is how many steps you took, even if you were going in circles, you’ve still walked miles in distance </li></ul>
7. 8. Position <ul><li>Where you are compared to origin </li></ul><ul><li>Can be (x meters, y meters) or x meters & r angle (degrees, radians) </li></ul><ul><li>Vector (magnitude & direction) </li></ul>
8. 9. (3,4)
9. 10. 5m, 53.13◦ AWE SOME
10. 11. <ul><li>A 2 + B 2 = C 2 (x coordinate 2 + y coordinate 2 = YES 2 ) </li></ul><ul><li>3 2 + 4 2 = C 2 </li></ul><ul><li>C = 5 </li></ul><ul><li>Cos(r) = 3/5 </li></ul><ul><li>Cos -1 Cos(r) = Cos -1 3/5 </li></ul><ul><li>r = 53.13 ◦ </li></ul>OH GOSH HOW DID I DO THAT?
11. 12. 10m 10m Distance = 3m + 1m = 4m Origin (0,0)
12. 13. <ul><li>Position IS NOT 4m </li></ul><ul><li>Distance travelled = 4m </li></ul><ul><li>Position = (-1, 3) </li></ul>STOP
13. 14. 10m 10m Distance = 3m + 1m = 4m Position = = m,108.43◦ Origin (0,0)
14. 15. 10m 10m Origin (0,0) ?
15. 16. Displacement <ul><li>Displacement = Δ position </li></ul><ul><li>Δ position = (x2 – x1)m + (y2 – y1)m </li></ul><ul><li>Original position (x1,y1) </li></ul><ul><li>New Position (x2,y2) </li></ul><ul><li>If the origin is the original position… :o </li></ul><ul><li>Position = displacement from origin </li></ul>
16. 17. 10m 10m Origin (0,0) Distance = 3m + 1m = 4m Displacement =-1mx + 3my Position = 6mx + 3my
17. 18. Another example <ul><li>Superman goes around the world </li></ul>“ superman that…”
18. 19. Superman’s Distance Superman’s Displacement Superman’s Position SUPERMAN THAT