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    A particle moves so that at time t seconds its position vector, r m , relative to a fixed origin is given by:

    r = (t^2-4t)i + (t^3 - at^2)j

    where a is a constant

    a) find an expression for the velocity of a particle at time t seconds
    b) tgiven that the particle comes to instantaneous rest, find the value of a

    cant do b, any help please
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    a) v = (2t-4)i + (3t²-2at)j

    b) 2t-4 = 0 => t = 2.

    => 3(2)² -2a(2) = 0 => a = 3
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    v= (2t-4)i + (3t²-2at)j

    comes to rest therefore v=0,

    therefore,

    2t-4=0
    3t²-2at=0

    from the first eqn, t=2

    putting t=2 in the 2nd eqn,

    3*4 - 2*a*2 = 0
    12 - 4a = 0
    a=3
    ==
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    (Original post by elpaw)
    a) v = (2t-4)i + (3t²-2at)j

    b) 2t-4 = 0 => t = 2.

    => 3(2)² -2a(2) = 0 => a = 3
    So when it comes to instantaneous rest the coeffecients of i and j(of the velocity vector) = 0 ?
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    (Original post by serious stuff)
    So when it comes to instantaneous rest the coeffecients of i and j(of the velocity vector) = 0 ?
    yes, thats what instantaneous rest means: the velocity is 0
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    (Original post by Fermat)
    v= (2t-4)i + (3t²-2at)j

    comes to rest therefore v=0,

    therefore,

    2t-4=0
    3t²-2at=0

    from the first eqn, t=2

    putting t=2 in the 2nd eqn,

    3*4 - 2*a*2 = 0
    12 - 4a = 0
    a=3
    ==
    how do you do r = (t^2-4t)i + (t^3 - at^2) ---> v= (2t-4)i + (3t²-2at)j im very bad at vectors
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    (Original post by elpaw)
    yes, thats what instantaneous rest means: the velocity is 0
    Yes but does instantaneous not imply that the time it takes for the velocity to get to 0 is 0?
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    (Original post by Illuvatar)
    how do you do r = (t^2-4t)i + (t^3 - at^2) ---> v= (2t-4)i + (3t²-2at)j im very bad at vectors
    differentiate the components wrt t
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    (Original post by serious stuff)
    Yes but does instantaneous not imply that the time it takes for the velocity to get to 0 is 0?
    no, instantenaous means momentary, i.e. it will not be 0 a moment later. for example, a ball thrown up in the air is at instantaneous rest at its maximum height
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    (Original post by elpaw)
    no, instantenaous means momentary, i.e. it will not be 0 a moment later. for example, a ball thrown up in the air is at instantaneous rest at its maximum height
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