This applet explores a parametric curve (or vector function) in [math]R^2[/math].

Enter the [b]i[/b] and [b]j[/b] components of your vector function in the textboxes, or choose an example from the dropdown menu. Drag the slider for t to trace out the path [b]r[/b](t), or click 'Animate' to trace out the path automatically.[br][br]What shape does the point [b]r[/b](t) trace out as t changes? Click 'Show parametric curve' to see the entire parametric curve.[br][br]You can add in the velocity [b]v[/b] and acceleration [b]a[/b] vectors using the checkboxes.[br][br]The 'Show i,j curves' checkbox shows the j-component as a function of t along the horizontal axis, and the i-component as a function of t along the vertical axis.