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Math Help - [SOLVED] Position and Velocity vector??

  1. #1
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    [SOLVED] Position and Velocity vector??

    Find the position and velocity vectors if the acceleration is
    A(t)= (cost)i -(tsint)k
    and the initial position and velocity vectors are R(0)=i-2j+k and V(0)=2i+3k respectively.

    Any help is appriciated, bla bla..
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  2. #2
    Super Member craig's Avatar
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    Quote Originally Posted by Lafexlos View Post
    Find the position and velocity vectors if the acceleration is
    A(t)= (cost)i -(tsint)k
    and the initial position and velocity vectors are R(0)=i-2j+k and V(0)=2i+3k respectively.

    Any help is appriciated, bla bla..
    Show us what work you have done so far, we can help you from there. bla bla
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  3. #3
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    Unfortunately, couldn't do anything on it.
    It looks gonna take integral of acceleration and put zero and gonna find velocity but i can not take the integral of vector. :S

    is it same as normal integral and put i , j , k? or does it exist something like integral of vector?
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  4. #4
    Super Member craig's Avatar
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    Quote Originally Posted by Lafexlos View Post
    Find the position and velocity vectors if the acceleration is
    A(t)= (cost)i -(tsint)k
    and the initial position and velocity vectors are R(0)=i-2j+k and V(0)=2i+3k respectively.

    Any help is appriciated, bla bla..
    To integrate a vector all you do is integrate the individual components.

    For example, a vector such as t^2 i + 3t j - 5k, differentiated with respect to  t would be, 2t i + 3 j.

    Hope this helps.

    Edit: The same rules for integration apply.
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  5. #5
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    Quote Originally Posted by craig View Post
    Show us what work you have done so far, we can help you from there. bla bla
    a(t) = (\cos{t})i - (t\sin{t})j

    i component ...

    you should already know the antiderivative of \cos{t}.

    j component ...

    you'll have to use integration by parts to find the antiderivative of t\sin{t}. give it a go.
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  6. #6
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    So, \int A(t)= (sint) i+ (c) j + (sint-tcost) k + C
    i think, now i should put zeros instead of t but when put zero for i component i get 0i but instant velocity has i component. Does it mean that  C has i component?
    Bah. Really confused but understand the logic. =) Thx for helps.
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  7. #7
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    You have forgotten the "constants of integration" for each component.
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  8. #8
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    Ok. I see.
    So it'll be (sint + C)i instead of (sint)i + C. Now everything is complete.
    Thx again for your helps.
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