This demo includes three graphical display windows.
The window "Parametric curve and velocity vector" displays the graph of
X(t) (which you can alter in the appropriately labeled textbox), the
point X(t0), and the velocity vector
X'(t0) with base X(t0).
The window "Graph of speed s'(t)" displays the graph of s'(t) =
||X'(t)|| in cyan, with the area shaded in blue below it representing
the integral of s'(t) from the minimum value of t to t0 or
the maximum value of t (depending on whether or not the "Show entire
curve" option is selected).
The window "Graph of arclength s(t)" displays the graph of s(t)
obtained by integrating s'(t) as displayed in the "Graph of speed
Change the value of t0 and other variables as in earlier demos.
As in earlier demos, there are "Show entire curve" and "Show Color Spectrum" options.
"Show Color Spectrum" also colors the velocity vectors, and the two speed graphs.