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 s'(t)" window.

To change t0, use the following buttons in the control window:

[<]: Decrease t0 by one step.
[>]: Increase t0 by one step.
[<<]: Decrease t0 until it reaches its minimum value.
[>>]: Increase t0 until it reaches its maximum value.

By default, the demo shows the point tracing out the curve, so that only part of it is shown. To show the entire curve, check the box "Show entire curve" by clicking on it.