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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

    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


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    The equation
    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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