A parametric curve has the coordinates given as a function of another variable which is often time.[br]As [math]t[/math] changes the position changes. This applet illustrates a two dimensional parametric function where the functions can be edited. The time [math]t[/math] is shown on a slider and the resulting position is shown as a point [br][math](x(t),y(t))[/math][br][br]Controls[br][b]t slider [/b]: shows and adjust the time [math]\left\{\text{time }|0\le t<2\pi\right\}[/math][br][b]x(t) [/b]: the the horizontal position function[br][b]y(t)[/b] : the vertical position function[br][b]Show Velocity [/b]: Will show the velocity vector on the right and left graphs.[br][b]Show Trace [/b]: Will plot a point or the position at each time[br][b]Show Curve [/b]: Will show a curve all of the positions for the time interval and a velocity curve if Show Velocity is on[br][b]Run : [/b]will continuously move the time from 0 to 2[math]\pi[/math], after clicking run a play/pause control will appear which can be used to pause and restart the time motion.[br][b]Show Acceleration[/b] : will replace the velocity curve with an acceleration point and curve[br]If Show Velocity or Show Acceleration are checked numerical values for position,velocity and acceleration in magnitude and angle form.[br]

Basically try the controls and a few different functions. The original function is periodic but what you enter does not need to be periodic. [br][br]With the original functions:[br]What are the maximum values of Position, Velocity and Acceleration?[br]How are these related to the 3 in the [math]x[/math] function?[br][br]Try the position functions x(t)=t/2 and y(t)= 2t-t^2/2.[br]What does this look like?