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Math Help - Vector Functions

  1. #1
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    Vector Functions

    I started working on this problem but dont really know where to go.

    The position function of a particle is given by .
    At what time is the speed minimum?

    I took the derivative of r(t) and got r'(t)=<-2t,-5,2t-4>. Where should i go from here? I dont really know what to do to solve for minimum t. Thanks for any help.
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  2. #2
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    Quote Originally Posted by palmaas View Post
    I started working on this problem but dont really know where to go.

    The position function of a particle is given by .
    At what time is the speed minimum?

    I took the derivative of r(t) and got r'(t)=<-2t,-5,2t-4>. Where should i go from here? I dont really know what to do to solve for minimum t. Thanks for any help.
    Speed is s(t)=\left\| {r'(t)} \right\| which an be made minimum.
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  3. #3
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    How do I figure out which t is minimum? Is is something like the first derivative test for regular functions?
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  4. #4
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    Quote Originally Posted by palmaas View Post
    How do I figure out which t is minimum? Is is something like the first derivative test for regular functions?
    That is exactly the way to go.

    P.S. This can really help you: s(t) = \left\| {r'(t)} \right\| \Rightarrow \quad s'(t) = \frac{{r'(t) \cdot r''(t)}}{{\left\| {r'(t)} \right\|}}
    Last edited by Plato; February 18th 2010 at 02:00 PM.
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  5. #5
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    Thanks! I use that and find a min at t=2/3. I tried that as an answer, but it does not show as correct. Did I end up doing something wrong? I got s'(t)= (12t-8)/sqrt(8t^2-16t+41)
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