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Math Help - Velocity

  1. #1
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    Velocity

    let v(t)=3t^2-12t be the velocity of a particle moving along the x axis for the time t, t>(greater than or equal) 0,
    When t=0,the particle is at x=-6

    A) determine the position of the particle at t=a
    B) write an expression for the speed of the particle at any time t
    C) in which direction does the particle begin moving and when does it turn around
    D) when, if ever, is the particle at the origin

    Ok so i haven't even attemt part A because I don't even know what a means, im guesing you have to integrate it somewhere tho
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  2. #2
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    Quote Originally Posted by rawkstar View Post
    let v(t)=3t^2-12t be the velocity of a particle moving along the x axis for the time t, t>(greater than or equal) 0,
    When t=0,the particle is at x=-6

    A) determine the position of the particle at t=a
    B) write an expression for the speed of the particle at any time t
    C) in which direction does the particle begin moving and when does it turn around
    D) when, if ever, is the particle at the origin

    Ok so i haven't even attemt part A because I don't even know what a means, im guesing you have to integrate it somewhere tho

    Right, for (A) , to find the position function ,namely p(t), you should integrate v(t) w.r.t. t :
    p(t)=\int v(t) \, dt = \int (3t^2-12t) \, dt=?
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  3. #3
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    p(t)=t^3-6t^2+C
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  4. #4
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    Quote Originally Posted by rawkstar View Post
    x(t)=t^3-6t^2+C
    note that the position function is x(t) (the position x as a function of time)

    now use your initial condition ...

    When t=0,the particle is at x=-6
    to find the constant of integration, C.
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  5. #5
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    ok x(0)=-6
    so that means that C=-6
    so x(t)=t^3-6t^2-6
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  6. #6
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    i still have no idea what a is
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  7. #7
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    Quote Originally Posted by rawkstar View Post
    i still have no idea what a is

    A) determine the position of the particle at t=a
    "a" is just a specific value of t

    x(a) = a^3-6a^2-6

    that's all.
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  8. #8
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    thank you
    i think i got it
    for B i just made my speed function f(x)=|3t^2-12t| since speed=|velocity|
    for C my answer was left then it changes to right @ 4
    for D my answer was approx 6.15
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