Traffic: Velocity 8

Traffic: Velocity 8
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2016-03-08 04:00
In collections Traffic
This example demonstrates the relationship between velocity in traffic flow and polynomial functions, visualizing velocity curves and tangent lines dynamically. Core math concepts include polynomial functions, conditional probability, calculus (derivatives, tangent lines, limits), vectors, and geometric constructions. Construction highlights use of Sequence and Segment commands for velocity curves/tangent segments, involving objects like functions f, polynomials f_1-f_3, parameter t, sliders a-k. Suitable for high school and above, exploring applications of calculus in physical phenomena and dynamic geometric modeling.

GeoGebra Commands & Parameters

  1. Sequence((n, f(n)), n, 0, t_1) → list1
  2. Sequence((n, g(n)), n, 0, t_1) → list2
  3. Segment((-1.9, 200), (-1.1, 200)) → g_3
  4. Segment((-1.9, 0), (-1.1, 0)) → e
  5. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  6. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  7. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  8. Sequence(x = i, i, 0, t_1) → mid_{road}
  9. Sequence(Translate[truck_p, Vector[(0, f(0)), (i, f(i))]], i, 0, t_1) → photo_b
  10. Sequence(Translate[bike_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r