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Math Help - Acceleration

  1. #1
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    Acceleration

    A particle moves in a straight line with a constant acceleration a m/s^2. At time t=0, the particle's velocity is u m/s.

    (a) Using the differential equation a=dv/dt, show that the velocity v, at time t is v=u+at.

    I haven't a clue what to do although it involves integration.
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  2. #2
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    Quote Originally Posted by Stuck Man View Post
    A particle moves in a straight line with a constant acceleration a m/s^2. At time t=0, the particle's velocity is u m/s.

    (a) Using the differential equation a=dv/dt, show that the velocity v, at time t is v=u+at.

    I haven't a clue what to do although it involves integration.
    get the equation into the form a dt = dv. now integrate both sides. you should get at + C = v since a is just a constant. the initial condition given to you says that at time t=0, v = u. so plug those in and you get a(0) + C = u or C = u.

    so therefore v = u + at
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  3. #3
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    I still don't understand. I haven't seen anything like this. I don't know why the book gives a question like nothing its covered before.
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  4. #4
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    Are you able to differentiate

    u + at

    with respect to t, assuming u and a are constants?
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  5. #5
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    I suppose I've understood. Thanks.
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