3 ms·

Yes: because the band is expanding both in-front of AND behind the ant, it will be much further on than X cm after X seconds. (Also: this is not a problem conc

by Roedou 13y ago

Yes: because the band is expanding both in-front of AND behind the ant, it will be much further on than X cm after X seconds. (Also: this is not a problem concerned with the physics of rubber or biology of ants. This ant is immortal, the rubber infinitely stretchy, etc.)

qwerty_asdf 13y ago
...then POINT A and POINT B are both in motion, simultaneously, while the ant is walking. Which is great, except that when the original concept is framed to the reader, the simple word problem doesn't specifically express that both ends are in motion. If both ends are in motion, then the ant's velocity changes. The ant might move 1 centimeter per second, relative to a fixed point in space, but it isn't moving 1 centimeter per second, relative to it's origin, POINT A. The motion of the rubber band is influencing the speed of the ant, relative to the band itself. Since the ant moves toward POINT B, while POINT A simultaneously accelerates away from the ant, the ant is moving faster than 1 centimeter per second, with each second spent traveling away from POINT A. Once this detail is added, it completely changes the premise of the problem. But the manner in which the problem is originally expressed is vague and incomplete, misleading the reader (perhaps deliberately so). Why would anyone claim the ant is moving 1 centimeter per second, RELATIVE TO THE ONLY OTHER FRAME OF REFERENCE IN THE PROBLEM (the rubber band), when its motion is clearly not 1 centimeter per second?
- cookingrobot 13y ago
  It doesn't make a difference in the solution if Point A is fixed or moving. The band is getting longer, and the and is standing on it - moving with it either way.
  - qwerty_asdf 13y ago
    It does matter, because if you tack Point A down to a fixed position, and pull Point B away at a fixed speed, and the ant's speed is explicitly measured as relative to it's distance from A, then ant isn't catching a ride on the rubber band. In that case, the ant is only moving at a fixed speed, toward the other end (100,000 times slower than the end's expansion), which will forever be too far away.
    - thedufer 13y ago
      The ant's speed is not explicitly measured relative to its distance from A. It is left unspecified what it is relative to, but the implication of "walking speed" (well, crawling speed, I guess) is that it is relative to the point of ground you are on.

by Roedou 13y ago

qwerty_asdf 13y ago

...then POINT A and POINT B are both in motion, simultaneously, while the ant is walking. Which is great, except that when the original concept is framed to the reader, the simple word problem doesn't specifically express that both ends are in motion. If both ends are in motion, then the ant's velocity changes. The ant might move 1 centimeter per second, relative to a fixed point in space, but it isn't moving 1 centimeter per second, relative to it's origin, POINT A. The motion of the rubber band is influencing the speed of the ant, relative to the band itself. Since the ant moves toward POINT B, while POINT A simultaneously accelerates away from the ant, the ant is moving faster than 1 centimeter per second, with each second spent traveling away from POINT A. Once this detail is added, it completely changes the premise of the problem. But the manner in which the problem is originally expressed is vague and incomplete, misleading the reader (perhaps deliberately so). Why would anyone claim the ant is moving 1 centimeter per second, RELATIVE TO THE ONLY OTHER FRAME OF REFERENCE IN THE PROBLEM (the rubber band), when its motion is clearly not 1 centimeter per second?

cookingrobot 13y ago
It doesn't make a difference in the solution if Point A is fixed or moving. The band is getting longer, and the and is standing on it - moving with it either way.
- qwerty_asdf 13y ago
  It does matter, because if you tack Point A down to a fixed position, and pull Point B away at a fixed speed, and the ant's speed is explicitly measured as relative to it's distance from A, then ant isn't catching a ride on the rubber band. In that case, the ant is only moving at a fixed speed, toward the other end (100,000 times slower than the end's expansion), which will forever be too far away.
  - thedufer 13y ago
    The ant's speed is not explicitly measured relative to its distance from A. It is left unspecified what it is relative to, but the implication of "walking speed" (well, crawling speed, I guess) is that it is relative to the point of ground you are on.