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Homework Help: Mechanics problem

  1. Aug 1, 2014 #1
    1. The problem

    A 3 kg object is moving in a plane with its x and y coordinates given by x = 5t^2 -1 and y = 3t^3 +2 where x and y are in meters and t is in seconds. Find the magnitude of the new force acting on this object at t= 2s

    2. My attempt.

    So my first attempt is to find a vector expression for acceleration. I integrated the expressions for x and y to give

    V subx = 5/3 t^3 -t +c

    To find the constant on integration I found the position of the particle at t=0 and t=2. Therefore calculating the velocity at 2 seconds. Thus the constant of integration for this expression is -4/3

    The velocity at 2s being 10i+12j ms^-1

    I have done the exact same process for velocity in the y direction and reached an expression for Vsuby .

    My problem is I'm not sure how to get a valid expression for acceleration, and this seems like a really long winded way of answering this question.
  2. jcsd
  3. Aug 1, 2014 #2
    If you have an expression ##\mathbf{r}(t) = (x(t), y(t))## for position, wouldn't velocity be ##\dot{ \mathbf{r}}## and acceleration ##\ddot {\mathbf{r}}##?
  4. Aug 1, 2014 #3

    Ray Vickson

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    Why are you integrating? How are force and acceleration related? Define acceleration!
  5. Aug 1, 2014 #4
    The net force on the object is the product of mass and acceleration. However I am being asked for the magnitude of the force on the object. I'm struggling to see how I can work with the expression for its displacement to get an expression for its acceleration so I can multiply its mass to get an expression for the net force
  6. Aug 1, 2014 #5


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    How is the position related to velocity? How is velocity related to acceleration?
  7. Aug 1, 2014 #6
    ImageUploadedByPhysics Forums1406907739.713390.jpg

    Got it! God I'm such a simpleton at times! I was inter grating when I should have been differentiating :(
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