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Tessminda · Nov 9, 2010, 08:35 AM

A magnetic train travelling at 33m/s [E] experiences an acceleration of 2.0m/s^2 [W] until it comes to rest. How long will it take the train to experience a displacement of 90.0m [E]? *Hint: there are two possible answers.*

ebaines · Nov 9, 2010, 09:15 AM

Use the basic formula:

$ x = x_0 + v_0 t + \frac 1 2 a t^2 $

Here you are given:

$ x = 90 m \\ x_0 = 0 m\\ v_0 = 33 \frac m s \\ a = - 2 \frac m {s^2} $

Note the sign of the acceleration value is negative, since the train is decelerating. You now have a quadratic equation that you can solve for t. Since it's a quadratic equation, there will be two answers. However, the problem states that it decelerates "until it coms to rest," so the second answer (which occurs AFTER the train has comes to rest and has actually started backing up) is not valid.

harum · Nov 9, 2010, 02:23 PM

This problem is not formulated properly. Because there are not two solutions, but infinitely many. Please ask whomever have offered you this problem what the direction of acceleration is compared to that of the given speed and what 90m-segment - out of infinitely many - has to be timed. This is a good example of how to turn a simple problem into hours of wasted time.

ebaines · Nov 9, 2010, 02:30 PM

Yes, it could be worded better, but I think the "E" and "W" symbols mean that the train is heading east (E) and accelerates toward the west (W). I think it's obvious that the question is asking how long it takes to move 90 m east from the point it starts decelerating (i.e, when it was moving at 33 m/s).