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Physics - Calculus Question

  1. Aug 2, 2010 #1
    Hi,

    here is my question:

    Potential energy = mgh
    Kinetic energy = 1/2mv^2
    mgh = 1/2mv^2, solving for v you get v = sqrt(2gh)

    Now I know v is the same as dx/dt so if I substite in dx/dt for v :

    dx/dt = sqrt(2gh)

    Multiply by dt:
    dx = sqrt(2gh) * dt
    Integrate:
    x = t*sqrt(2gh)

    This should be right, but for some reason it doesnt work when I check it with the well known x = x0 + v0t + 1/2at^2 formula, what am I doing wrong?
     
  2. jcsd
  3. Aug 2, 2010 #2
    h is dependent on t, ie it's not a constant. What you calculated is if a ball fell a height h under gravity, and then started moving at constant velocity (at which point you say t=0) then the ball would move x = t*sqrt(2gh) in time t.
     
  4. Aug 3, 2010 #3
    Oh I see, thanks for your help!
     
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