Velocity and Acceleration Vectors on Parametric Curve

Velocity and Acceleration Vectors on Parametric Curve
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2015-06-21 00:07
This example demonstrates the decomposition of velocity and acceleration vectors into components parallel and perpendicular to the position vector on a parametric curve. Key math concepts include vector decomposition, parametric equations, derivatives, and the geometric interpretation of velocity and acceleration vectors. It utilizes GeoGebra commands like Derivative, CurveCartesian, Textfield, and If, focusing on vector analysis and the application of calculus in geometry, suitable for high school and above.

GeoGebra Commands & Parameters

  1. Derivative(g) → g'
  2. Derivative(g') → g''
  3. Derivative(f) → f'
  4. Derivative(f') → f''
  5. CurveCartesian(f(t), g(t), t, tmin, tmax) → c
  6. CurveCartesian(f'(t), g'(t), t, tmin, tmax) → cdot
  7. CurveCartesian(f''(t), g''(t), t, tmin, tmax) → cddot
  8. Textfield(tmin) → Tmin
  9. Textfield(tmax) → Tmax
  10. Textfield(f) → FofT
  11. Textfield(g) → GofT
  12. If(togA ≟ 1, "Stop Animation", "Start Animation") → Animate
  13. Textfield(speed) → SPD
  14. Textfield(t) → tEq