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Velocity, Position, and Acceleration vs. Time Graphs by Tom Walsh

Velocity, Position, and Acceleration vs. Time Graphs by Tom Walsh
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2014-09-26 03:50
FunctionCalculusGraphing
In collections animation Constructions
This example demonstrates how adjusting a Velocity vs. Time graph dynamically updates the corresponding Position vs. Time and Acceleration vs. Time graphs. Key math concepts include function graphs, special points, and the calculus relationship between velocity, position, and acceleration. Constructed using GeoGebra commands like Segment, Point, and Midpoint. Suitable for high school and above students learning kinematics and function graph relationships, or for physics instruction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_3
  2. Point(a_3) → R
  3. Segment((5, -4), (5, 4)) → m1
  4. Point(m1) → E
  5. Segment((6, -4), (6, 4)) → m2
  6. Point(m2) → F
  7. Segment(E, F) → a
  8. Segment((9, -4), (9, 4)) → m5
  9. Segment((8, -4), (8, 4)) → m4
  10. Segment((7, -4), (7, 4)) → m3
  11. Midpoint(a_3) → D
  12. Segment(D, C) → b
  13. Segment(A_1, B_1) → a_1
  14. Midpoint(a_1) → D_1
  15. Segment(D_1, C_1) → b_1
  16. Segment(A_2, B_2) → a_2
  17. Midpoint(a_2) → D_2
  18. Segment(D_2, C_2) → b_2
  19. Point(m3) → G
  20. Segment(F, G) → c
  21. Point(m4) → H
  22. Segment(G, H) → d
  23. Point(m5) → I
  24. Segment(H, I) → e
  25. Segment(J, K) → f
  26. Segment(K, L) → g
  27. Segment(L, M) → h
  28. Segment(M, N) → i
  29. Segment(N, O) → j
  30. Segment(O, P) → k
  31. Segment(P, Q) → l

AI Drawing Prompt Reference

Draw velocity-time, position-time, and acceleration-time graphs that dynamically update. Start by drawing a horizontal segment with perpendicular segments extending upward and downward from its ends to form a cross. Then add horizontal segments on both sides of the cross and mark key points on these segments. Finally, connect these points to form the graphs for velocity, position, and acceleration, showing their relationships.
The prompt above was compiled from the original drawing commands and is for reference only.