course

On Problem #1 you correctly say that `ds = 1/2 (v0 + vf) * `dt, then you conclude that 2 `ds * `dt = v0 + vf; should be 2 `ds / `dt = v0 + vf. Using your expression you find that v0 = 1/2 `dt ( a - 2 `ds ). Should be v0 = `ds / `dt - 1/2 a `dt, which is the same as your expression v0 = (`ds - 1/2 a `dt^2) / `dt. Either way this says that the initial velocity differs from the average velocity `ds / `dt by half the change in velocity a `dt. Note among other things that the units of `dt * `ds are not the same as those of velocity.

You did an excellent analysis on #2; this would be an excellent analysis for a Phy 231 student. One note on notation, though: when using derivatives you wouldn't use a' and a'' for anything but the derivatives of a. For the actual and functional accelerations you could use, for example, a and a with the symbol ~ over the top.

Problem 3 was a straightforward interpretation of slope and area, and you did everything right.

On #4, you wouldn't assume that the object came to rest in .331 seconds, since this would result in an acceleration different than the given acceleration. Your alternatives are acceleration +6 cm/s^2 and -6 cm/s^2 (you were given only the magnitude). Since the object is going up the incline, the negative acceleration would be appropriate, and you would set the problem up as you did in the first part but using negative accel.

Then to get the distance up the incline, you would use the initial velocity you found in the first part, and you would assume vf = 0, with the acceleration still -6 cm/s^2. Your method of setting the derivative of the position function equal to 0 would work fine with this information.

Most students need feedback on the corresponding 'daily quiz' problem to see what to do here. My comments here should clarify your work on Week 4 Quiz 2.

Good solution on #5. I generally don't count this one against Phy 121 students, but of course give full credit (and in fact a little extra credit) for those who do get it.

Your Week 5 Quiz 1 was very good, but your final result for `dt on the second ramp was incorrect. I suspect you used the length of the ramp rather than the acceleration in your expression `dt2 = (vf2 - v02) / a2. Should have come out a little over 1 second (26 cm/s to 41 cm/s averages around 33 cm/s so it takes a bit over a second to travel 39 cm; also vel change is about 15 cm/s so at 13 cm/s^2 accel it will take a bit over a second).

You're obviously in good shape for the Major Quiz. Your work is in fact consistent with the Phy 231 level.

I'm glad you enjoy the challenge of my courses. My goal is to provide a reasonable level of expectation at the C level with a high level of expectation at the A level, so that an average student at a less selective institution will tend to make a C in my course as easily as at their college or university, while my A's are consistent with A level work at the more selective public universities in Va (e.g., UVA or Tech).

Phy 121 students do need a lot of practice to do well on the Major Quiz, and often need multiple attempts on some of the Weekly Quiz problems. I don't expect them to completely master the material, though some do and I wouldn't want to deprive them of the challenge. Others simply learn to recognize the different situations, which are reasonably predictable, and get through by a combination of imitation and understanding. After the Major Quiz, the tests get easier and more predictable for 121 students; the opposite is the case for 231 students, who usually ace the Major Quiz with only minor errors. The 201 falls somewhere in between; usually the highest grade in that course is on the Major Quiz.

Assigned text problems for 121 students are more than 50% Level I problems and don't include any of the more challenging Level II problems. The 231 text has problems which are mostly similar to those in the 201 text, but about half a level more challenging, and of course include calculus-based problems. The level of my expectation for a 231 student is much higher than for a 201 student. Usually the calculus-based problems aren't that difficult for a calculus-literate student; the things that give 231 students trouble are largely the things that give 201 students trouble.