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Time Motion - Increasing Velocity: A Grid Referenced by Velocity and Acceleratio

Time Motion - Increasing Velocity: A Grid Referenced by Velocity and Acceleratio
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2016-02-20 06:14
VectorTransformationGeometric ConstructionSlider AnimationGraphing
In collections Complex Math
This GeoGebra example demonstrates a time-based motion model with increasing velocity, where a custom grid system is constructed using velocity and acceleration as reference axes. It visually illustrates how position, velocity, and acceleration evolve over time, emphasizing the vector nature of motion. Core mathematical concepts include vectors, velocity and acceleration as directed quantities, kinematics relationships, and geometric transformations such as reflection and orthogonal projection. The construction employs GeoGebra commands including Vector for drawing velocity/acceleration arrows, Point, Segment, and Line for basic elements, OrthogonalLine and Intersect to create perpendicular reference lines and their intersections, Mirror for symmetry, Polygon for area construction, and multiple text objects (text1–text7) for labeling key values. This resource is suitable for high school physics or mathematics lessons on kinematics and vector geometry, as well as introductory college mechanics, helping learners grasp uniformly accelerated motion and vector decomposition through interactive visualization.

GeoGebra Commands & Parameters

  1. Vector((a, 0)) → u
  2. Vector((a, 0), (a, b)) → v
  3. Vector((a, 0), (a, c)) → w
  4. Point(w) → E
  5. Segment(C, E) → l
  6. Point(v) → F
  7. Segment(C, F) → m
  8. Vector((b, 0), (b, f)) → n
  9. Vector((b, 0), (b, g)) → p
  10. Point(p) → G
  11. Point(n) → D
  12. Segment(C, G) → j
  13. Segment(C, D) → k
  14. Point(u) → I
  15. Line(G, j) → q
  16. Line(F, w) → r
  17. Point(q) → J
  18. Point(u) → K
  19. OrthogonalLine(J, xAxis) → d_1
  20. Intersect(s, t) → P
  21. Segment(C, P) → a_1
  22. Intersect(t, yAxis) → Q
  23. Segment(Q, P) → b_1
  24. Segment(T, P) → c_1
  25. Segment(S, A_1) → e_1
  26. Segment(R, Z) → f_1
  27. Segment(U, B_1) → g_1
  28. Segment(V, C_1) → h_1
  29. Segment(C, W) → i_1
  30. Mirror(C, c_1) → C'
  31. Mirror(W, c_1) → W'
  32. Segment(C', W') → j_1
  33. Mirror(R, c_1) → R'
  34. Mirror(Z, c_1) → Z'
  35. Segment(R', Z') → k_1
  36. Mirror(S, c_1) → S'
  37. Mirror(A_1, c_1) → D_1
  38. Segment(S', D_1) → l_1
  39. Mirror(Q, c_1) → Q'
  40. Mirror(P, c_1) → P'
  41. Segment(Q', P') → m_1
  42. Mirror(V, c_1) → V'
  43. Mirror(C_1, c_1) → E_1
  44. Segment(V', E_1) → n_1
  45. Mirror(U, c_1) → U'
  46. Mirror(B_1, c_1) → F_1
  47. Segment(U', F_1) → p_1
  48. Mirror(S', j_1) → S''
  49. Mirror(D_1, j_1) → G_1
  50. Segment(S'', G_1) → q_1
  51. Mirror(R', j_1) → R''
  52. Mirror(Z', j_1) → Z''
  53. Segment(R'', Z'') → r_1
  54. Mirror(Q', j_1) → Q''
  55. Mirror(P', j_1) → P''
  56. Segment(Q'', P'') → s_1
  57. Mirror(V', j_1) → V''
  58. Mirror(E_1, j_1) → H_1
  59. Segment(V'', H_1) → t_1
  60. Mirror(U', j_1) → U''
  61. Mirror(F_1, j_1) → I_1
  62. Segment(U'', I_1) → a_2
  63. Mirror(S'', s_1) → S'''
  64. Mirror(G_1, s_1) → K_1
  65. Segment(S''', K_1) → b_2
  66. Mirror(V'', s_1) → V'''
  67. Mirror(H_1, s_1) → J_1
  68. Segment(V''', J_1) → c_2
  69. Mirror(U'', s_1) → U'''
  70. Mirror(I_1, s_1) → L_1
  71. Segment(U''', L_1) → d_2
  72. Mirror(R'', s_1) → R'''
  73. Mirror(Z'', s_1) → Z'''
  74. Segment(R''', Z''') → e_2
  75. Segment(C, E) → f_2
  76. Segment(C, F) → g_2
  77. Polygon(A_2, B_2, C_2, D_2) → poly1, a_3, b_3, c_3, d_3
  78. Segment(E_2, F_2) → p_2
  79. Vector((1, 0), (l_3, l_3) / ((12 * 54))) → v_2

AI Drawing Prompt Reference

Draw a dynamic grid system referenced by velocity and acceleration, illustrating uniformly accelerated motion. Start from the origin, draw a horizontal velocity vector, then from its endpoint draw an acceleration vector and another velocity-change vector upward. Based on these vectors, construct multiple points, segments, and perpendicular lines to form orthogonal reference lines. Use mirror operations to reflect some segments and points across a slanted line, creating symmetric geometric structures. Finally, add polygons and text labels for key values, showing how position, velocity, and acceleration evolve over time.
The prompt above was compiled from the original drawing commands and is for reference only.