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Math Help - find the velocity vector for an object

  1. #1
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    find the velocity vector for an object

    find the velocity vector for an object having

    \vec a(t) = e^t  \hat{j} -32 \hat{k}

    if

    v(0) = 3 \hat{i} - 2 \hat{j} + \hat{k}

    Im not sure how to proceed. Would i integrate? How to handle the v(0) has me confused!

     v(t) = \int e^t  \hat{j} -32 \hat{k}\    dt

     v(t) =  e^t j -32t k + c

    Im not sure if i am doing this correctly?
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    Re: find the velocity vector for an object

    Quote Originally Posted by icelated View Post
    Im not sure if i am doing this correctly?
    Yes. The initial velocity, \mathbf v(0), is an initial condition. Use it to determine the constant of integration.

    \mathbf v(t) = e^t\mathbf j-32t\mathbf k + \mathbf C

    So

    \mathbf v(0) = 3\mathbf i - 2\mathbf j + \mathbf k

    \Rightarrow e^0\mathbf j-32\cdot0\mathbf k + \mathbf C = 3\mathbf i - 2\mathbf j + \mathbf k

    \Rightarrow\mathbf C = 3\mathbf i - 3\mathbf j + \mathbf k
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    Re: find the velocity vector for an object

    Would i then integrate again?

    Here is the final answer, but i cant seem to get to it

    v(t) = 3i +(e^t - 3)j +( -32t +1)k
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    Re: find the velocity vector for an object

    Quote Originally Posted by icelated View Post
    Would i then integrate again?
    Why would you?

    Quote Originally Posted by icelated View Post
    Here is the final answer, but i cant seem to get to it

    v(t) = 3i +(e^t - 3)j +( -32t +1)k
    Just substitute what you (I) found for \mathbf C back into the equation for \mathbf v(t). That's it.
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    Re: find the velocity vector for an object

    I can see that now! Thank you..
    Problems like this in the book integrate. ybe if v(0) = 0?
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