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Math Help - Mechanics Problem 2 - Vectors

  1. #1
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    Mechanics Problem 2 - Vectors

    A particle has an intial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds.

    Im completely stuck and don't know where to start!! Thanks for your help.
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  2. #2
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    Quote Originally Posted by MingMing View Post
    A particle has an intial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds.

    Im completely stuck and don't know where to start!! Thanks for your help.
    Since you know the direction of the acceleration you know that

    \mathbf{a}=s(\mathbf{i}+\mathbf{j}) but you also know that

    \sqrt{\mathbf{a} \cdot \mathbf{a}}=5\sqrt{2}=\sqrt{2s^2}=|s|\sqrt{2} \implies s=5

    This gives the acceleration vector as

    \mathbf{a}=5\mathbf{i}+5\mathbf{j}

    Can you finish from here?
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  3. #3
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    Quote Originally Posted by MingMing View Post
    A particle has an intial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds.

    Im completely stuck and don't know where to start!! Thanks for your help.
    Similar to your other problem \displaystyle \vec{v} = \vec{v_0} + \vec{a}t

    The acceleration vector will be the unit vector in the direction of i + j times its magnitude.

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TheEmptySet View Post
    \mathbf{a}=5\mathbf{i}+5\mathbf{j}
    For the record, this is not the acceleration. This is \displaystyle \vec{a}t. (Which, of course, you can use as well. )

    -Dan
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  5. #5
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    Got it
    Last edited by MingMing; March 6th 2011 at 10:52 AM.
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