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Math Help - Mechanics Question

  1. #1
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    Mechanics Question

    A particle of mass 3kg, moves along the horizontal x-axis under the action of a resultant force FN. Its velocity V m/s at time t s.

    v=12t-3t

    a) given that the particle is at the origin O when t=1, find an expression for the displacement of the particle from O at the time t s.

    b) Find the acceleration of the particle at time t s.

    c) Find the power of the force F when t=1.5


    right for part a I think i am supposed to integrate v so i do

    ∫12t-3t dt (Is this correct? as in am i supposed to write dt? or dx?)

    this gives me the result x=6t-t where x = displacement

    Is this the answer?

    For part b do i differentiate the original equation?

    No sure how to do part C

    Any help welcome =]
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  2. #2
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    Hey,

    You're perfectly right about parts a and b, with a) you need to integrate with t going from 0 to 1.

    For part c) you need to use The equation F=ma where F is the force, m is mass and a is acceleration.

    Hope that helps.
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  3. #3
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    Quote Originally Posted by hairymclairy View Post
    Hey,


    For part c) you need to use The equation F=ma where F is the force, m is mass and a is acceleration.
    For Part C the Power is given by

    P(t) =F(t).v(t)

    Where p is power v is velocity and f is force at time t

    Hope this adds to that help
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  4. #4
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    thanks for helping. So before i attempt part c, are the answers to parts a and b:

    a) x=6t-t

    b) A= 12-6t

    where you said t going from 0 to 1, are these the limits to put on the integral?


    also would the answer to part c be 101.25W ?
    Last edited by mr fantastic; March 13th 2009 at 05:44 PM. Reason: Merged posts
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by djmccabie View Post
    A particle of mass 3kg, moves along the horizontal x-axis under the action of a resultant force FN. Its velocity V m/s at time t s.

    v=12t-3t

    a) given that the particle is at the origin O when t=1, find an expression for the displacement of the particle from O at the time t s.

    b) Find the acceleration of the particle at time t s.

    c) Find the power of the force F when t=1.5


    right for part a I think i am supposed to integrate v so i do

    ∫12t-3t dt (Is this correct? as in am i supposed to write dt? or dx?)

    this gives me the result x=6t-t where x = displacement

    Is this the answer?

    For part b do i differentiate the original equation?

    No sure how to do part C

    Any help welcome =]
    Displacement = ∫12t-3t dt

    <br />
S(t) = 12(t^2)/2 - 3(t^3)/3 + c

    Now put the limit from 0 to 1

    S(1) - S(0) = 6 - 1 = 5m

    ----------------------------

    v=12t-3t

    Acceleration = \frac{dv}{dt}

    = 12 - 6t

    -----------------------------------

    Power = F(t).v(t)

    =3a(t).v(t) = 3(12-6t)(12t-3t^2)

    Now put  t= 1.5s
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  6. #6
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    Projectiles

    thanks
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