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速度、距离与时间在运动中的可视化：RACE CAR示例

速度、距离与时间在运动中的可视化：RACE CAR示例
几何画板及绘图内容加载中，请稍等……
2015-06-03 18:22
向量解析几何几何作图
所属专题 Primary School Mathematics Collection
这个范例通过模拟多辆汽车的运动，帮助学生直观理解速度、距离与时间之间的关系。核心数学概念包括速度公式、位移计算和总距离累积。作图要点涉及使用GeoGebra命令如Simplify、If、Min、Max、Textfield、Segment和Polygon来构建汽车位置、位移和总距离。适合初中或高中学生用于学习运动学基础和几何作图技能。

GeoGebra 命令及参数

  1. Simplify(YellowPositionInput) → YellowPosition
  2. Simplify(Integral[abs(Derivative[YellowPosition])]) → YellowTotalDistanceFromZero
  3. Simplify(RedPositionInput) → RedPosition
  4. Simplify(Integral[abs(Derivative[RedPosition])]) → RedTotalDistanceFromZero
  5. Simplify(GreenPositionInput) → GreenPosition
  6. Simplify(Integral[abs(Derivative[GreenPosition])]) → GreenTotalDistanceFromZero
  7. Simplify(YellowPosition(x) - YellowPosition(x_1)) → YellowDisplace
  8. Simplify(YellowTotalDistanceFromZero(x) - YellowTotalDistanceFromZero(x_1)) → YellowTotalDistance
  9. If(ShowPosition ≟ true, YellowPosition, If[ShowDisplacement ≟ true, YellowDisplace, If[ShowTotalDistance ≟ true, YellowTotalDistance, 0]]) → YellowCar
  10. Simplify(RedPosition(x) - RedPosition(x_1)) → RedDisplace
  11. Simplify(RedTotalDistanceFromZero(x) - RedTotalDistanceFromZero(x_1)) → RedTotalDistance
  12. If(ShowPosition ≟ true, RedPosition, If[ShowDisplacement ≟ true, RedDisplace, If[ShowTotalDistance ≟ true, RedTotalDistance, 0]]) → RedCar
  13. Simplify(GreenPosition(x) - GreenPosition(x_1)) → GreenDisplace
  14. Simplify(GreenTotalDistanceFromZero(x) - GreenTotalDistanceFromZero(x_1)) → GreenTotalDistance
  15. If(ShowPosition ≟ true, GreenPosition, If[ShowDisplacement ≟ true, GreenDisplace, If[ShowTotalDistance ≟ true, GreenTotalDistance, 0]]) → GreenCar
  16. Simplify(BluePositionInput) → BluePosition
  17. Simplify(BluePosition(x) - BluePosition(x_1)) → BlueDisplace
  18. Simplify(Integral[abs(Derivative[BluePosition])]) → BlueTotalDistanceFromZero
  19. Simplify(BlueTotalDistanceFromZero(x) - BlueTotalDistanceFromZero(x_1)) → BlueTotalDistance
  20. If(ShowPosition ≟ true, BluePosition, If[ShowDisplacement ≟ true, BlueDisplace, If[ShowTotalDistance ≟ true, BlueTotalDistance, 0]]) → BlueCar
  21. Min(BlueCar, x_1, x_2) → BlueMinPoint
  22. Max(BlueCar, x_1, x_2) → BlueMaxPoint
  23. Min(GreenCar, x_1, x_2) → GreenMinPoint
  24. Max(GreenCar, x_1, x_2) → GreenMaxPoint
  25. Min(RedCar, x_1, x_2) → RedMinPoint
  26. Max(RedCar, x_1, x_2) → RedMaxPoint
  27. Min(YellowCar, x_1, x_2) → YellowMinPoint
  28. If(NumberOfCars ≟ 1, Min[{y(RedMinPoint)}], If[NumberOfCars ≟ 2, Min[{y(RedMinPoint), y(BlueMinPoint)}], If[NumberOfCars ≟ 3, Min[{y(RedMinPoint), y(BlueMinPoint), y(GreenMinPoint)}], If[NumberOfCars ≟ 4, Min[{y(RedMinPoint), y(BlueMinPoint), y(GreenMinPoint), y(YellowMinPoint)}]]]]) → MinFunctionValue
  29. Max(YellowCar, x_1, x_2) → YellowMaxPoint
  30. If(NumberOfCars ≟ 1, Max[{y(RedMaxPoint)}], If[NumberOfCars ≟ 2, Max[{y(RedMaxPoint), y(BlueMaxPoint)}], If[NumberOfCars ≟ 3, Max[{y(RedMaxPoint), y(BlueMaxPoint), y(GreenMaxPoint)}], If[NumberOfCars ≟ 4, Max[{y(RedMaxPoint), y(BlueMaxPoint), y(GreenMaxPoint), y(YellowMaxPoint)}]]]]) → MaxFunctionValue
  31. If(NumberOfCars ≟ 1, Max[{RedCar(x_2)}], If[NumberOfCars ≟ 2, Max[{RedCar(x_2), BlueCar(x_2)}], If[NumberOfCars ≟ 3, Max[{RedCar(x_2), BlueCar(x_2), GreenCar(x_2)}], If[NumberOfCars ≟ 4, Max[{RedCar(x_2), BlueCar(x_2), GreenCar(x_2), YellowCar(x_2)}]]]]) → MaxEndValue
  32. If(MaxFunctionValue ≥ MaxEndValue + FinishBlockWidth + (1 / 10 * CarLength), 0, FinishBlockWidth + (1 / 10 * CarLength)) → RightScreenCushion
  33. Textfield(x_1) → inputBox2
  34. Textfield(x_2) → inputBox3
  35. Segment(TLT, TRT) → TrackTopLine
  36. Segment(BLT, BRT) → TrackBottomLine
  37. Polygon(BLT, BLSB, TLSB, TLT) → StartingBlockOutline, blt_2, blsb_1, tlsb_1, tlt_1
  38. Polygon(BRFB, BRT, TRT, TRFB) → FinishBlockOutLine, brfb, brt_1, trt_1, trfb
  39. Textfield(NumberOfCarsTemp) → inputBox1
  40. If(NumberOfCars > 3, true, false) → ShowYellowCar
  41. If(NumberOfCars > 2, true, false) → ShowGreenCar
  42. If(NumberOfCars > 1, true, false) → ShowBlueCar
  43. If(NumberOfCars > 0, true, false) → ShowRedCar
  44. Textfield(RedPositionInput) → RedInputBox
  45. Textfield(BluePositionInput) → BlueInputBox
  46. Textfield(GreenPositionInput) → GreenInputBox
  47. Segment(LOL, LOR) → LaneOne
  48. Segment(LTL, LTR) → LaneTwo
  49. Segment(LThL, LThR) → LaneThree
  50. Textfield(YellowPositionInput) → inputBox7
  51. If(NumberOfCars ≟ 1, {RedCar}, If[NumberOfCars ≟ 2, {RedCar, BlueCar}, If[NumberOfCars ≟ 3, {RedCar, BlueCar, GreenCar}, If[NumberOfCars ≟ 4, {RedCar, BlueCar, GreenCar, YellowCar}]]]) → ListOfCars
  52. If(NumberOfCars ≟ 1, Min[{RedCar(x_1)}], If[NumberOfCars ≟ 2, Min[{RedCar(x_1), BlueCar(x_1)}], If[NumberOfCars ≟ 3, Min[{RedCar(x_1), BlueCar(x_1), GreenCar(x_1)}], If[NumberOfCars ≟ 4, Min[{RedCar(x_1), BlueCar(x_1), GreenCar(x_1), YellowCar(x_1)}]]]]) → MinStartValue

AI 绘图提示语参考

画一个赛车比赛的赛道，赛道由两条平行的直线构成，上方一条为TrackTopLine，下方一条为TrackBottomLine。赛道两端各有起始和终点标志，起始标志由StartingBlockOutline构成，终点标志由FinishBlockOutLine构成。赛道中间有四条车道，分别用LaneOne、LaneTwo、LaneThree和LaneFour表示，每条车道上有一辆赛车，分别是RedCar、BlueCar、GreenCar和YellowCar。用户可以通过输入框输入每辆赛车的位置，显示位置、位移或累计距离。
以上提示语为根据原始绘图命令整理而来，仅供参考。