非均匀直线运动与恒定加速度

非均匀直线运动与恒定加速度
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2015-01-14 02:56
本范例演示了非均匀直线运动与恒定加速度的关系。核心数学概念包括直线运动、加速度和速度。通过使用GeoGebra命令如Point、Polygon、Segment等,可以构造出运动物体的位置、速度和加速度曲线。适合高中物理和数学教学。

GeoGebra 命令及参数

  1. Point(yAxis) → A_1
  2. Point(yAxis) → B_1
  3. Polygon(A_1, C_1, D_1, B_1) → poli1, a_1, c, d, b_1
  4. Point(b_1) → A
  5. PointIn(poli1) → F
  6. PointIn(poli1) → G
  7. PointIn(poli1) → B
  8. PointIn(poli1) → C
  9. PointIn(poli1) → D
  10. PointIn(poli1) → E
  11. Segment(A, B) → e
  12. Segment(B, C) → f
  13. Segment(C, D) → g
  14. Segment(D, E) → h
  15. Segment(E, F) → i
  16. Segment(F, G) → j
  17. Intersect(e, xAxis) → H
  18. Intersect(f, xAxis) → I
  19. Intersect(g, xAxis) → J
  20. Intersect(h, xAxis) → K
  21. Intersect(i, xAxis) → L
  22. Intersect(j, xAxis) → M
  23. Slope(e) → A1
  24. Slope(f) → A2
  25. Slope(g) → A3
  26. Slope(h) → A4
  27. Slope(i) → A5
  28. Slope(j) → A6
  29. Segment((x(A), A1), (x(B), A1)) → l
  30. Segment((x(B), A2), (x(C), A2)) → n_2
  31. Segment((x(D), A3), (x(C), A3)) → p
  32. Segment((x(D), A4), (x(E), A4)) → q
  33. Segment((x(F), A5), (x(E), A5)) → r
  34. Segment((x(F), A6), (x(G), A6)) → s
  35. CurveCartesian(t, (y(A) * t) + (A1 * t^(2) / 2), t, 0, x(B)) → v
  36. CurveCartesian(t, spo1 + (y(B) * (t - x(B))) + (A2 * (t - x(B))^(2) / 2), t, x(B), x(C)) → u
  37. CurveCartesian(t, spo1 + spo2 + (y(C) * (t - x(C))) + (A3 * (t - x(C))^(2) / 2), t, x(C), x(D)) → w
  38. CurveCartesian(t, spo1 + spo2 + spo3 + (y(D) * (t - x(D))) + (A4 * (t - x(D))^(2) / 2), t, x(D), x(E)) → z
  39. CurveCartesian(t, spo1 + spo2 + spo3 + spo4 + (y(E) * (t - x(E))) + (A5 * (t - x(E))^(2) / 2), t, x(E), x(F)) → c_1
  40. CurveCartesian(t, spo1 + spo2 + spo3 + spo4 + spo5 + (y(F) * (t - x(F))) + (A6 * (t - x(F))^(2) / 2), t, x(F), x(G)) → d_1
  41. OrthogonalLine(B, xAxis) → e_1
  42. OrthogonalLine(C, xAxis) → f_1
  43. OrthogonalLine(D, xAxis) → g_1
  44. OrthogonalLine(E, xAxis) → h_1
  45. OrthogonalLine(F, xAxis) → i_1
  46. Max(A10, 0, x(B)) → B10
  47. Max(A11, x(B), x(C)) → B11
  48. Max(A12, x(C), x(D)) → B12
  49. Max(A13, x(D), x(E)) → B13
  50. Max(A14, x(E), x(F)) → B14
  51. Max(A15, x(F), x(G)) → B15
  52. Min(A10, 0, x(B)) → D10
  53. Min(A11, x(B), x(C)) → D11
  54. Min(A12, x(C), x(D)) → D12
  55. Min(A13, x(D), x(E)) → D13
  56. Min(A14, x(E), x(F)) → D14
  57. Min(A15, x(F), x(G)) → D15
  58. Max(lista2) → D1
  59. Min(lista3) → D2
  60. Min(lista1) → A7
  61. Max(lista1) → A8
  62. Point(p) → N
  63. Point(n_2) → O
  64. Point(l) → P
  65. Point(r) → Q
  66. Point(s) → R
  67. Point(q) → S
  68. Point(v) → T
  69. Point(u) → U
  70. Point(w) → V
  71. Point(z) → W
  72. Point(c_1) → Z
  73. Point(d_1) → E_1
  74. If(m ∧ (¬n), Min[A7, -5] - 1, If[n ∧ (¬m), Min[D2, -5] - 1, If[m ∧ n, Min[lista5] - 1, -6]]) → ymin
  75. If(m ∧ (¬n), Max[A8, 5] + 1, If[n ∧ (¬m), Max[D1, 5] + 1, If[m ∧ n, Max[lista4] + 1, 6]]) → ymax
  76. OrthogonalLine(G, xAxis) → b

AI 绘图提示语参考

画一个演示非匀速直线运动与恒定加速度关系的图形。首先绘制一个五边形,然后在该五边形上取六个点,依次连接这些点形成线段。接着,计算每条线段的斜率,并基于斜率和点的位置绘制五条平行线段。最后,用这些线段和五边形构建出速度和加速度曲线,展示非匀速直线运动的特点。
以上提示语为根据原始绘图命令整理而来,仅供参考。