MathPlotAI Logo MathPlotAI

Non Uniform Linear Motion with Constant Acceleration

Non Uniform Linear Motion with Constant Acceleration
Loading the math board and drawing, please wait…
2015-01-14 02:56
FunctionCoordinate GeometrySlider Animation
In collections Prof. Stick's Mostly Good Guide to Physics
This example illustrates the relationship between non-uniform linear motion and constant acceleration. Key mathematical concepts include linear motion, acceleration, and velocity. Using GeoGebra commands such as Point, Polygon, Segment, etc., the position, velocity, and acceleration curves of a moving object can be constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a graph illustrating the relationship between non-uniform linear motion and constant acceleration. Start by creating a pentagon, then place six points on it and connect these points with line segments. Calculate the slope of each segment and draw five parallel line segments based on these slopes. Finally, use the segments and the pentagon to construct velocity and acceleration curves, showcasing the characteristics of non-uniform linear motion.
The prompt above was compiled from the original drawing commands and is for reference only.