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Physics Olympiad Vector Acceleration

  1. Jan 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle of mass 2.00 kg moves under a force given by
    F~ = −(8.00 N/m)(xˆi + yˆj)
    whereˆi and ˆj are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity~v = (3.00 m/s)ˆi + (4.00 m/s)ˆj.

    a. After how much time will the particle first return to the origin?
    b. What is the maximum distance between the particle and the origin?



    2. Relevant equations
    f=ma
    x=vt+1/2at^2


    3. The attempt at a solution
    Using f=ma, i find the acceleration to be a=-4x i + -4y j
    Using x=vt+1/2at^2, if i set x as 0
    So i get 0=3t+1/2(-4x)t^2 and 0=4t+1/2(-4y)t^2
    I solve those 2 equtaions to get 3y=4x
    but i don't know where to continue
     
  2. jcsd
  3. Jan 11, 2012 #2

    SammyS

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    The equation
    x=vt+(1/2)at2
    has 2 big problems.
    1. It's only true for uniform (constant) acceleration. The acceleration here is not constant.

    2. Even if the acceleration were constant you should only have included x components.​
     
  4. Jan 11, 2012 #3
    hm do i use calculus?
    a= derivative of x
     
  5. Jan 11, 2012 #4
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