anonymous
  • anonymous
A particle moves on a straight line v(t)=sinwt cos ^{3} wt. find the position s(t) if s(0)=0. I've done this style of question before, but the two variables throw me off. I assume that u=cos(wt) but am unsure.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
then du=-sin(wt)
anonymous
  • anonymous
-du=sin(wt)
anonymous
  • anonymous
\[- \int\limits_{?}^{?} (u)^{3} du\]

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anonymous
  • anonymous
\[-\frac{ 1 }{ 4 } (u)^{4} +c\]
anonymous
  • anonymous
\[- \frac{ (coswt)^{4} }{ 4 } +c\] then insert s(0)=0 so..... \[- \frac{ (cosw(0))^{4} }{ 4 } +c\]=0 ... but w is still an unknown...
anonymous
  • anonymous
woooooooo no idea whats going on....
anonymous
  • anonymous
unless -cosw(0)=0... then c=0... yeah i'm confused, doesn't seem right.
sirm3d
  • sirm3d
\[\mathrm du=-w\cdot\sin wt\,\mathrm dt\]

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