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Parametrization 2D
Use the slider t or the run-button to move the point A along the path in 2D.
The application shows the three following vectors:
r : Position Red - r(t) = [x(t),y(t)] = [f(t),g(t)]
v : Velocity Blue - The derivative of the position vector
a : Acceleration Green - The derivative of the velocity vector
The r-vector = [f(t),g(t)] can be changed,
the same of the minimum/maximum of the parameter t
The scale-slider can be used to adjust the length of the velocity and acceleration.
Try these parametric curves:
r(t) = [x(t),y(t)] = [5cos(t),5sin(t)]
r(t) = [x(t),y(t)] = [5cos(t),3sin(t)]
r(t) = [x(t),y(t)] = [t,t]
r(t) = [x(t),y(t)] = [2t,2t]
r(t) = [x(t),y(t)] = [t,0.5t2]
r(t) = [x(t),y(t)] = [t,sin(t)]
r(t) = [x(t),y(t)] = [3(t-sin(t),3(1-cos(t)]
Link to GeoGebra library.
Link to programming code.
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