Comments regarding the parameterized curves project:

• I saw lots of very good work, some truly outstanding. However, many also had some significant deficiencies that I would like to see fixed. The due date for reworked projects is Wed Sep 11. Those who did not turn in any work this week, will be able to earn 2/3=66.6% credit, two students who turned in very minimal work this week may earn 3/4=75% credit, while all others have the opportunity to earn full 100% of the missing credit (incl. bonus points for the acceleration).
• Since everyone has the chance to make up for missed points, I graded, what for many was the first draft, quite strictly. Total 30 pts + 5 bonus (for accelaration formulas + arrows). Deductions -10 for overlapping time intervals,- 5 each for missing formulas and/or missing arrows for velocity, - 15 for missing computer printout of the plots (i.e. to demonstrate that the formulas are indeed correct, do what they are designed to do). This meant that some students got 0 points for this first draft even though they turned in quite a bit of correct work. Fix it and get full credit next week.
• Regarding parameterizations: Every curve can be reparameterized so that its parameter t takes values in any desired interval! If you plan ahead -- think ahead -- it should be quite easy to change your parameterizations so that there are no overlapping time intervals.
• Re velocity, I prefer to obtain a formula for dR/dt that is of the same form as the formula for the curve R(t), i.e. using braces to combine several "pieces". Once you have got this, it is so easy to get (piecewise) formula for the acceleration as well -- get the easy points!
• Re plotting the velocity -- in this context, v and a should be plotted as arrows, attached at appropriate points along the curve. Make sure that the directions agree with your formulas. On the other hand, there is no reason to use the same scales for the magnitudes of the velocity, acceleration and position vectors -- think about their respective dimensions!!!!!