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Speed as the Derivative of Position

Speed as the Derivative of Position
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2016-08-03 18:34
VectorCalculusDerivative
This example demonstrates the interpretation of the derivative as the speed of a vehicle. The core mathematical concept is the derivative. It uses Circle, Vector, Derivative, Rotate, Textfield, Segment, Midpoint, etc., GeoGebra commands/objects. Suitable for high school math education or learning the concept of derivatives.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Vector(A, B) → u
  3. Derivative(e) → v
  4. Rotate(u, ((-3 * π / 2) * v(t) / 160)) → u'
  5. Textfield(t_0) → CajaDeEntrada1
  6. Segment((e_0, 0), (e_0, 2)) → a
  7. Segment((e_{t1}, 0), (e_{t1}, 2)) → b
  8. Vector((0, 1.8), (e_{t1}, 1.8)) → w
  9. Vector((0, 2), (e_0, 2)) → d
  10. Midpoint((e_0, 2), (e_{t1}, 2)) → C

AI Drawing Prompt Reference

Draw a coordinate plane illustrating the derivative of position as speed. Start with a circle centered at a point with another point on its circumference, and draw a vector from the center to that point. Add a curve representing position over time and its derivative curve. Rotate the vector by an angle proportional to the derivative value at a specific time to show velocity direction. Include a text input field to adjust the time parameter. Mark two time points on the horizontal axis, draw vertical segments of height 2 at each. From y=1.8, draw a horizontal vector to the second time point, and from y=2, draw a horizontal vector to the first time point, then mark the midpoint of these two vectors.
The prompt above was compiled from the original drawing commands and is for reference only.