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Math Help - finding how far something has gone

  1. #1
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    finding how far something has gone

    ok this problem seems easy but it still is giving me problems.

    A particle that moves along a straight line has velocity v(t) = t^2e^-(2t)

    meters per second after t seconds. How many meters will it travel during the first t seconds?
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  2. #2
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    Quote Originally Posted by mbrez88 View Post
    ok this problem seems easy but it still is giving me problems.

    A particle that moves along a straight line has velocity v(t) = t^2e^-(2t)

    meters per second after t seconds. How many meters will it travel during the first t seconds?
    Since v(t) > 0 for all t, the particle does not change direction and so the distance travelled after the first t seconds is the same as the displacement x after the first t seconds.

    Since v = \frac{dx}{dt} you're expected to calculate x = \int t^2 e^{-2t} \, dt. Integration by parts (twice) is one approach that could be used. To get the constant of integration, you can assume x = 0 when t = 0.
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  3. #3
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    Quote Originally Posted by mbrez88 View Post
    ok this problem seems easy but it still is giving me problems.

    A particle that moves along a straight line has velocity v(t) = t^2e^-(2t)

    meters per second after t seconds. How many meters will it travel during the first t seconds?
    \int_0^t x^2 \cdot e^{-2x} \, dx

    integration by parts ... tabular method should make it easier.

    \left[-\frac{e^{-2x}}{4}\left(2x^2 + 2x + 1\right)\right]_0^t
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