This demo includes two windows. The first displays the curve X(t) that
you can alter in the
appropriately labeled textbox, the point X(t_{0}), and the
velocity vector
X'(t_{0}) with base X(t_{0}). The second window
displays the velocity vector
X'(t_{0}) with its base at the origin and the curve X'(t_{0})
traced out by the head
of the vector. You also have the option of showing the
acceleration vector X''(t_{0}) tangent to the curve in the
second window
at the point X'(t_{0}) by clicking the appropriate checkbox in
the control
window.

Change the value of t_{0} and other variables as in earlier demos.

As in earlier demos, there are "Show entire curve" and "Show Color Spectrum" options.
"Show Color Spectrum" will also color the velocity vector and the velocity curve.