anonymous
  • anonymous
Find the error? Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 2sin\(^2\) t, y = 2cos\(^2\) t, 0 ≤ t ≤ 4π I can't see what I did wrong here, posting image below. Any idea @TuringTest? The derivatives look ok...
Physics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
*Fixed the formatting syntax in the question
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=8pi

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anonymous
  • anonymous
It's a full two revolutions, obviously. What stumps me is what I could have done incorrect here when the other problem around it are ok... *goes to see your link*
anonymous
  • anonymous
8\(\pi\)? o_O What about it?
experimentX
  • experimentX
why ... what is the answer?
anonymous
  • anonymous
A smart way to see this problem is check that \[x ^{2}+y^{2}=4\]. This is an equation for the circunference with radius R=2. Since \[4 \pi \] means two revolutions, the length of the circunference is \[S=2\pi R\] then the distance traveled is \[8\pi \]. Note that the displacement is zero, because the initial and end position are same while the distance traveled is not zero in this case.

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