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Traffic: Velocity 4

Traffic: Velocity 4
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2016-03-08 03:57
FunctionTrigonometryCoordinate GeometryOptimizationParametric Equation
In collections Traffic
This example demonstrates the dynamic relationship between traffic flow velocity and parametric equations. It involves core math concepts like piecewise functions, parametric curves, orthocenter, correlation, and optimization problems. Construction highlights include using GeoGebra commands Sequence and Segment with objects like g_4, g_2, t, a, b, c, d, list2. Suitable for high school and above students studying parametric equations, function graphs, and optimization applications.

GeoGebra Commands & Parameters

  1. Sequence((n, g(n)), n, 0, t_1) → list2
  2. Segment((-1.9, 0), (-1.1, 0)) → road_0
  3. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  4. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  5. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  6. Sequence(x = i, i, 0, t_1) → mid_{road}
  7. Sequence(Translate[car_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r
  8. Segment((-1.9, 200), (-1.1, 200)) → road_{200}

AI Drawing Prompt Reference

Draw a traffic flow velocity diagram with a road from -1.9 to -1.1, with 0.4 unit wide lines on both sides and a middle line. Above the road, draw a car moving with velocity changing by position, using parametric equations and piecewise functions. Also draw a horizontal line above the road at 200 units height.
The prompt above was compiled from the original drawing commands and is for reference only.