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Math Help - Stuck ? help

  1. #1
    Junior Member
    Joined
    Sep 2008
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    Stuck ? help

    The acceleration in ms-2 ofa body starting from restis given by

    f(t)= 1/10te^0.1t
    Determine the velocity of the body after 20 seconds
    Do not know where to start
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  2. #2
    Member Mentia's Avatar
    Joined
    Dec 2008
    From
    Bellingham, WA
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    Remember:

     \ddot {x(t)} = \dot {v(t)} = a(t)

    Then:

    v =  \int_{ }^{ } a(t)dt

    So we have:

    a(t) = \frac {t}{10}e^{\frac {t}{10}}

    We also know that v(0) = 0 since the body starts from rest.

    Then:

    v(t) = \int_{ }^{ } \frac {t}{10}e^{\frac {t}{10}}

    This can be done by parts if you want. You get:

    v(t) = e^{t/10} (t-10) + c.

    Plug in your initial condition:

    0 = (0 - 10) + c.

    Then,

    c = 10.

    Then,

    v(t) = e^{t/10} (t-10) + 10.

    If you want the velocity at t = 20, you have:

    v(20) = e^{20/10} (20-10) + 10 = (10e^{2}+10) \frac {m}{s}
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  3. #3
    Junior Member
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    thanks for your help,I am slowly getting to grips with it.
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