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Position, Velocity, and Acceleration vs. Time Graphs

Position, Velocity, and Acceleration vs. Time Graphs
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2019-06-22 02:31
FunctionCalculusGraphing
This example demonstrates how changes in a velocity-time graph affect the corresponding position-time and acceleration-time graphs. It covers basic calculus concepts such as derivatives and integrals. GeoGebra commands used include slider animation, locus, and function graphing. Suitable for high school and above students.

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 a velocity-time graph where velocity is 0 at 5 seconds and 6 seconds, then draw position-time and acceleration-time graphs. The slope of the velocity graph corresponds to changes in the position graph, and the slope of the position graph corresponds to changes in the acceleration graph. Use slider animation to change the velocity graph and observe the changes in the position and acceleration graphs.
The prompt above was compiled from the original drawing commands and is for reference only.