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Speed, Distance & Time in Motion (RACE CAR)

Speed, Distance & Time in Motion (RACE CAR)
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2015-06-03 18:22
VectorCoordinate GeometryGeometric Construction
In collections Primary School Mathematics Collection
This example demonstrates the concept of speed, distance, and time through a simulation of multiple cars. It involves mathematical concepts such as velocity, displacement, and cumulative distance. The construction uses GeoGebra commands like Simplify, If, Min, Max, Textfield, Segment, and Polygon to visualize car positions, displacements, and total distances. Suitable for middle or high school students learning kinematics and geometric construction.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a race track with two parallel lines, the top line is TrackTopLine and the bottom line is TrackBottomLine. At both ends of the track, there are starting and finishing markers, with StartingBlockOutline for the start and FinishBlockOutLine for the finish. In the middle of the track, there are four lanes represented by LaneOne, LaneTwo, LaneThree, and LaneFour, each with a car: RedCar, BlueCar, GreenCar, and YellowCar. Users can input the position of each car in the text fields to show position, displacement, or total distance.
The prompt above was compiled from the original drawing commands and is for reference only.