This demo includes two windows. The first displays the curve X(t) that you can alter in the appropriately labeled textbox, the point X(t0), and the velocity vector X'(t0) with base X(t0). The second window displays the velocity vector X'(t0) with its base at the origin and the curve X'(t0) traced out by the head of the vector. You also have the option of showing the acceleration vector X''(t0) tangent to the curve in the second window at the point X'(t0) by clicking the appropriate checkbox in the control window. To move the point X(t0) along the curve, 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. Click on the "Show position vector X(t0)" box to show the position vector X(t0) whose components are the coordinates of the point X(t0).