Question 4 Walkthrough

1. Replace the "15.0" in the "Seconds:" box with "10.0".
2. Press the radio button "Quadratic B" and then press "Redraw". Several multicolored dots should appear on the graph.
3. The yellow and green dot at the origin means that we want the yellow (velocity) and green (position) graphs to pass through this dot, which they automatically do anyway. We need the green graph to pass through the green dot at (10,250) and we need the yellow and red graphs to pass through the red/yellow dot at (10,0).
4. We want a quadratic acceleration, so replace the "1.0" in the box after "A:" with "0".
5. It turns out that careful solution leads to

   a(t) = 0.9t² - 12t + 30.

   Plug in "0.9" for B, "-12" for C, and "30" for D and press "Redraw". All three graphs should go through their respective target dots.
6. To run the simulation, move the slider bar about two-thirds of the way from "Slow" to "Fast".
7. Now press "Go!" and notice how the car glides safely to the wall.
8. To see what happens when things go amiss, enter "300" for D and press "Go!".
9. Another possibility: Try "10" for D and see what happens.