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High Speed Train Trip as Piecewise Linear Function

High Speed Train Trip as Piecewise Linear Function
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2019-01-25 06:23
FunctionCoordinate GeometryCalculusGeometric ConstructionSlider Animation
In collections TFM: Introducción al Cálculo Infinitesimal (1º Bachillerato)
This example demonstrates the kinematics of a high-speed train trip using piecewise linear functions. It covers key concepts such as piecewise functions and linear functions. Using GeoGebra commands like Intersect, Segment, and OrthogonalLine, the construction of piecewise linear functions is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(f1, xAxis, (164.28191428571427, 0)) → A
  2. Intersect(f1, yAxis, (0, 620)) → B
  3. Segment(C, D) → g
  4. OrthogonalLine(C, g) → h
  5. OrthogonalLine(D, g) → i
  6. Intersect(f1, i, (20, 567.50035)) → J
  7. Intersect(f1, h, (10, 602.5)) → K
  8. OrthogonalLine(E, g) → j
  9. OrthogonalLine(F, g) → k
  10. OrthogonalLine(C, xAxis) → l
  11. OrthogonalLine(G, g) → m
  12. OrthogonalLine(H, g) → n
  13. OrthogonalLine(C, xAxis) → p
  14. OrthogonalLine(N, g) → q
  15. OrthogonalLine(L, g) → r
  16. OrthogonalLine(M, g) → s
  17. OrthogonalLine(I, g) → t
  18. Intersect(f1, t, (152.5, 20.62368749999996)) → O
  19. Intersect(f1, s, (142.5, 55.628675000000044)) → P
  20. Intersect(f1, r, (105, 252.5)) → Q
  21. Intersect(f1, q, (95, f1(95))) → R
  22. Intersect(f1, n, (85, 304.9937)) → S
  23. Intersect(f1, m, (80, 304.99649999999997)) → T
  24. Intersect(f1, k, (70, 322.49895000000004)) → U
  25. Intersect(f1, j, (60, 357.50104999999996)) → V
  26. Segment(K, C) → e
  27. Segment(J, D) → f_1
  28. Segment(V, E) → g_1
  29. Segment(U, F) → h_1
  30. Segment(S, H) → i_1
  31. Segment(T, G) → j_1
  32. Segment(R, N) → k_1
  33. Segment(Q, L) → l_1
  34. Segment(P, M) → m_1
  35. Segment(I, O) → n_1
  36. Point(f11) → Z
  37. Point(f11) → A_1

AI Drawing Prompt Reference

Draw a diagram of a high-speed train trip using piecewise linear functions. Start by plotting a curve representing speed changes, then construct a series of perpendicular lines and segments based on intersections with the x-axis and y-axis. Highlight the formation of piecewise linear functions through these constructions, including multiple line segments, perpendiculars, and intersection points, forming various triangles and trapezoids to illustrate different stages of the train's motion.
The prompt above was compiled from the original drawing commands and is for reference only.