I have questions.   Inquiring minds want to know . . .

Do you have to have a canoe to canoodle?

When LEDs (light emitting diodes) fail, do they become DEDs (dark emitting diodes)?

If train A leaves Philadelphia at 10:30 am traveling at 55 mph, and train B leaves Memphis at 12:15 pm  traveling at 72 mph,  how do the trains accelerate from 0 mph to their respective cruising speeds instantaneously?

Do you have answers?  If you do, please send them to me via the comments.


About cweenmj

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7 Responses to Questions

  1. publius says:

    Serious answer to silly question:

    Because the time taken to accelerate to constant velocity is small compared to the duration of the journey, it can be effectively neglected for computation purposes.

    Assume that the train leaving Memphis starts at zero miles per hour, and accelerates at the sedate rate (!) of one foot per second per second — remember that gravitation acts at thirty-two feet per second per second. It then requires 105.6 seconds to reach its cruising speed, less than two minutes. From Memphis to Chicago, where you meet the train from Philadelphia, is 520 miles by the AMTRAK schedule, or 7 hours 13 minutes 20 seconds at a constant 72 mph. In 105.6 seconds accelerating at 1 ft/s^2, the train covers 5575.68 ft or 1.056 mile. Assume an identical deceleration at Chicago, and you have 311.2 s spent between 0 and 72 mph, and 25 894.4 s spent at 72 mph.

    The total time is then 7 hours 16 minutes 45.6 seconds. The difference of 3 minutes 25.6 seconds is only 78/100 of 1%, or in other words, enough time for the train to travel just over four miles at top speed. The difference is not going to lead to any serious error for most users, especially when random “noise” factors such as line delays are added in. For this reason, the calculation neglecting acceleration & deceleration can be used safely — it is not much less realistic, but is much less time-consuming, than the calculation including them.

  2. cweenmj says:

    Why, thank you, publius!!
    That’s one question down, two to go. And I thought that would be the hard one to answer!!

  3. publius says:

    Serious answer to silly question:

    When a light-emitting diode fails, it is normally due to “junction breakdown”. In other words, it ceases to emit light because it has ceased to be a diode. From then on, it will conduct electricity in either direction subject to a slight ohmic loss. A component which behaves in this way is known as a “resistor”.

  4. Cweenmj says:

    Hhmmpf. I suppose you are going to put the cabash on canoodling in a canoe, too. 😉

  5. Mark Taylor says:

    Silly answers to serious questions: Pubelicus is quite likely right but he seems to know so much that he knows nuthin at all.

    LEDs remain LEDs after they have burned out except that they are no longer ‘light emitting diodes’, they become ‘light eating diodes’.

    The train problem is obvious, nothing ever said that the trains were stopped in their respective cities. Train A entered Philadelphia at 10:27 traveling at 55MPH and three minutes later left Philadelphia at the same speed. You can obviously extrapolates for train 2.

    Regarding the canoodling. I have a canoe that was made by Old Towne sometime back in the 1960’s that I can no longer take camping, the damned thing is too big. It’s 18 feet long and weighs over 90 pounds but it is the most wonderful canoe I own (I have several). It is all fiberglass and there are no thwarts between the forward and the aft seats, it is rather beamy, will carry one half ton of crew and gear, has enough keel for easy paddling on long hauls, is incredibly stable, & I have the mast, sail, leeboards, and rudder for sailing it (it’s fast but tricky). It is so stable in fact, that my ex and I actually did some serious canoodling in it while camping on an island in the Adirondacks some 30 years ago and our son was born about 3/4 year later. So while you don’t need a canoe for canoodling, it surely doesn’t hurt.

    I love your site, I love your binary/hex link from LOLCATS and I really like that I am allowed to hang out with some really smart, very clever, and obviously good people like you and the Cheezfrendz. KTHXBAI.

  6. cweenmj says:

    Hai mark,
    hoo R U on ICHC?

  7. LyP says:

    A probably silly question to publius:

    Although the four-mile difference is “not much less realistic, but is much less time-consuming, than the calculation including them” won’t it matter to someone standing less 3.5 miles away?

    Or probably I’ve got that wrong, won’t it matter if there is a timer on board that causes something to blow up three minutes earlier than the train will stop so everyone can get off?

    Anyway, thanks for this great question and excellently written answer! I can actually understand it, and I typically have difficulty following problem statements of this type. I wish you had written all my word problems when I was in math in the Long Ago Tyme!

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