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Math Help - Maths Mechanics SUVAT mechanics

  1. #1
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    Maths Mechanics SUVAT mechanics

    A train starts from rest at a station and after 30 seconds stops at the next station, 500m away.

    If distance travelled in time T is given by, s = cT^2(k-T) where c and k are constants...

    i) Find formulae for velocity and acceleration.

    velocity:
    v=s/t so, = cT(k-T) ???

    acceleration:
    s=ut + 1/2at^2
    cT^2(k-T)=0 + 1/2at^2
    a=2c(k-T) ???

    ii)Use the fact that velocity is zero when T=30 to find value of k.
    v=30c(k-30)=0
    30ck=900c
    k=30

    iii)Use the fact that s=500 when T=30 to find c.

    The problem here is the (k-T) part of every formula, where k and T are both 30, giving 0... suggesting that k shouldn't be 30?


    (not sure what forum to post this in)
    Any and all help is greatly appreciated! Many thanks.
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  2. #2
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    Quote Originally Posted by fbird67 View Post
    A train starts from rest at a station and after 30 seconds stops at the next station, 500m away.

    If distance travelled in time T is given by, s = cT^2(k-T) where c and k are constants...

    i) Find formulae for velocity and acceleration.

    velocity:
    v=s/t so, = cT(k-T) ???

    s = ckT^2 - cT^3

    v = s' = 2ckT - 3cT^2
    = cT(2k - 3T)

    acceleration:
    s=ut + 1/2at^2 ... this equation only works if acceleration is a constant
    cT^2(k-T)=0 + 1/2at^2
    a=2c(k-T) ???

    a = v' = 2ck - 6cT = 2c(k - 3T)

    now, recalculate the following ...

    ii)Use the fact that velocity is zero when T=30 to find value of k.

    iii)Use the fact that s=500 when T=30 to find c.
    .
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  3. #3
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    Ah, OK. Thanks a lot, that was a great help.
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