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Why aren't the derivatives equal?

  1. Oct 14, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-10-13_23-28-41.png

    2. Relevant equations
    see above

    3. The attempt at a solution
    After getting ##v = |\frac{dz}{dt}|=\frac{3}{t^2+1}## why can't I simply take the derivative of that with respect to ##t## to get the acceleration?
    ]
     
  2. jcsd
  3. Oct 14, 2015 #2

    Mark44

    Staff: Mentor

    The notation is a little weird. What they're calling v is actually the magnitude of the velocity, not the velocity itself, and ##\frac{dz}{dt}## is the velocity. To get the acceleration, you need to differentiate the velocity (not its magnitude) with respect to t.
     
  4. Oct 14, 2015 #3
  5. Oct 14, 2015 #4
    Okay, so simply put the derivative of the magnitude of velocity is not the magnitude of acceleration? ##\frac{d}{dt}(|\frac{dz}{dt}|)\neq|\frac{d^2 z}{dt^2}|##
     
  6. Oct 14, 2015 #5
    But the question asks for the magnitude of acceleration
     
  7. Oct 14, 2015 #6

    Mark44

    Staff: Mentor

  8. Oct 14, 2015 #7

    Mark44

    Staff: Mentor

    Right, but they first have to get the acceleration, and then get its magnitude.
     
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