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For what value of x will this object first come to rest?

  1. Mar 23, 2015 #1
    1. The problem statement, all variables and given/known data
    A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (–4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?

    2. Relevant equations
    0.5 mv^2 = KE
    F*d = work

    3. The attempt at a solution
    Since KE = 0.5 * 2 * 5^2 = 25J
    and F*d = -4.0x^2
    -4x^2 = 25J
    x = 2.5 m
    This is how I approached it, but the answer is 3.5m. Can anyone help me out?
     
  2. jcsd
  3. Mar 23, 2015 #2
    Since the force changes with x, what will be the work done by the force when the body moves by a distance dx?
    Integrate it to find the total work and the expression you get comes out to be different. why?
    you cant find the net work done like this:
    everything else is correct. Just the left hand side of the equation.
     
  4. Mar 23, 2015 #3
    Oh I got it now
    Fxdx = -4.0x dx
    W = -2.0x^2 J = 0.5 * 2 * 5^2 J
    x = 3.5m right??
    Thank you so much!
     
  5. Mar 23, 2015 #4
    The force changes as the position of particle changes. So you can't get the value of work done by simply multiplying F with x.
     
  6. Mar 23, 2015 #5
    Got it now!! Thank you for helping me!!
     
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