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Thread: particle moving

  1. #1
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    particle moving

    A particle of mass 6 kg starts from rest and is subject to a force which increases uniformly from 0N to 12N in a time of 20s. prove the acceleration of the particle is t/10 m/s^2 seconds after it begins to move. prove that after the particle has moved a distance s meters when its speed is v m/s then
    9s^2 =20v^3

    I am not sure how to set this up. I can not use f=ma or P=FV
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  2. #2
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    Re: particle moving

    There are very few problems in physics where you can't use $F=m a$

    This is not one of them.

    You're given mass. You're given force as a function of time. Therefore you are given acceleration as a function of time.

    The rest is a bit of straightforward calculus.
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    Re: particle moving

    So this is what I did

    so the force varies over time and we not one of the conditions. so I said F=Kt where k is a constant which we do not know and t is time. so the question says the force is 12N when t is20

    so 12=20k 3/5 =k so then using F=ma 3/5 *t =6a a=t/10

    I then let dv/dt and I let the upper limits be t and v and I rearranged to get t=√(20v)

    so i then let t/10 = v dv/ds and I subbed in t=√(20v) and I integrated this and I got a useless expression. I thought I did every thing right and I can not see where I went wrong
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    Re: particle moving

    Quote Originally Posted by edwardkiely View Post
    So this is what I did

    so the force varies over time and we not one of the conditions. so I said F=Kt where k is a constant which we do not know and t is time. so the question says the force is 12N when t is20

    so 12=20k 3/5 =k so then using F=ma 3/5 *t =6a a=t/10

    I then let dv/dt and I let the upper limits be t and v and I rearranged to get t=√(20v)

    so i then let t/10 = v dv/ds and I subbed in t=√(20v) and I integrated this and I got a useless expression. I thought I did every thing right and I can not see where I went wrong
    ok so you got $a(t) = \dfrac {t}{10}$

    simple calculus gets you

    $v(t) = \dfrac{t^2}{20}$

    $s(t) = \dfrac{t^3}{60}$

    $v(T) = V$

    $T^2 = 20V$

    $T = \sqrt{20V}$

    $s(T) = S$

    $T^3 = 60S$

    $T = (60S)^{1/3}$

    $(20V)^{1/2} = (60S)^{1/3}$

    $8000V^3 = 3600S^2$

    $20V^3 = 9S^2$
    Thanks from edwardkiely
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    Re: particle moving

    thank you
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