This applet explores a parametric curve (or vector function) in .
Enter the i and j 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 r(t), or click 'Animate' to trace out the path automatically. What shape does the point r(t) trace out as t changes? Click 'Show parametric curve' to see the entire parametric curve. You can add in the velocity v and acceleration a vectors using the checkboxes. 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.