Parametric Curve in the Plane


A parametric curve has the coordinates given as a function of another variable which is often time. As changes the position changes. This applet illustrates a two dimensional parametric function where the functions can be edited. The time is shown on a slider and the resulting position is shown as a point Controls t slider : shows and adjust the time x(t) : the the horizontal position function y(t) : the vertical position function Show Velocity : Will show the velocity vector on the right and left graphs. Show Trace : Will plot a point or the position at each time Show Curve : Will show a curve all of the positions for the time interval and a velocity curve if Show Velocity is on Run : will continuously move the time from 0 to 2, after clicking run a play/pause control will appear which can be used to pause and restart the time motion. Show Acceleration : will replace the velocity curve with an acceleration point and curve If Show Velocity or Show Acceleration are checked numerical values for position,velocity and acceleration in magnitude and angle form.
Basically try the controls and a few different functions. The original function is periodic but what you enter does not need to be periodic. With the original functions: What are the maximum values of Position, Velocity and Acceleration? How are these related to the 3 in the function? Try the position functions x(t)=t/2 and y(t)= 2t-t^2/2. What does this look like?