I found in Physics Today (January 1999), pages 26 to 30, the following
question of the Force Concept Inventory, "a 29-question test that has
helped increase awareness of the extent of student conceptual difficulties
in mechanics":
The positions of two blocks at successive 0.20-second time intervals
are represented by the numbered squares in the diagram below.
The blocks are moving toward the right.
20. Do the blocks ever have the same speed?
(A) No.
(B) Yes, at instant 2.
(C) Yes, at instant 5.
(D) Yes, at instants 2 and 5.
(E) Yes, at some time during interval 3 to 4.
The graphic did not come out clear. You could see it in Physics Today,
January 1999, page 27.
When I saw it, I read it rapidly and found the right answer. Some
colleagues of mine and myself are writing classnotes for a precalculus
course in Physics. Two of the teachers and I are writing the Kinematics
chapter with a conceptual focus that finds resistance in the rest of the
group. So, I translated it to Spanish and tested the whole group on it,
asking them to choose the correct answer *and* explain it. It seems that
the evaluation is going to fail due to the translation that I made of the
following line: "Do the blocks ever have the same speed?" I translated the
word "ever" as "always", and not as "at any time". I am afraid I made a
mistake in the translation of the word "ever". Anyway, three teachers
answered (A) "The initial conditions are unknown (?)"; another answered (A)
"They travel different distances at equal time intervals"; another answered
(A) "The first block has variable speed and the second one has constant
speed"; another answered (D) "By definition(?)". Even though there seems to
be a mistake in the translation of the word "ever", one out of seven
answered correctly (E) "The speed of block B is constant. The speed of A is
increasing. So, at some instant the speed of A must equal the speed of B."
My answer was (E) because the average speed of the upper block and of the
lower block during interval 3 to 4 is the same and equal to 80 units of
lenght / second, the speed of the lower block is constant and of the upper
block is increasing during the interval and if their average speeds are
equal it means that at some time during interval 3 to 4 the blocks have the
same instantaneous speed equal to 80 units of lenght / second. (It is easier
to explain with the Mean Value Theorem of Calculus). I would like to know
your explanations. I am not as much interested in the answer itself as in
the efficient *use* of the concepts.
Finally, could you tell me if the wording of the test question is correct
and if my translation ruined the test. And, does somebody has access to the
whole Force Concept Inventory? I'll appreciate too your insights about a
"conceptual focus on kinematics", the larger and mostly mathematical
chapter. I would like to share to you our presentation of the chapter.