In this animation t is the time and s is the blue point's coordinate. Click the play button (small triangle) in the lower left to start the point in motion. If you pause the motion, you can see the blue point's coordinate at a particular time by dragging the small black point or by typing "t =" some value into the input line. Clicking the double arrow icon in the upper right will reset the applet.

1. When does the particle seem to be moving the fastest? [br]2. Is the particle ever stopped between t = 0 and t = 4.5? If so, when?[br]3. For what values of t is the particle moving left?[br]4. Make a graph of the particle's position, s, as a function of time, t.[br]5. What is the particle's average velocity from t = 0 to t = 4.5?[br]6. What is the particle's average velocity from t = 2 to t = 3?[br]7. What is the particle's average velocity from t = 2 to t = 2.1?[br]8. What is the particle's average velocity from t = 2 to t = 2.01[br]9. What is the particle's average velocity from t = 2 to t = 2.001?[br]10. What is the particle's velocity at the instant when t = 2?[br]11. Make a graph of the particle's velocity as a function of time.

Box Folding Problem - Maximizing Volume[br][br]A piece of cardboard is rectangular. We cut a square that is [i]h[/i]" square from each corner and fold up the sides to form a box. What length should [i]h[/i] be to maximize the volume of the box?