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Equation of motion problem

  1. Jul 16, 2008 #1
    1. The problem statement, all variables and given/known data
    The position of a particle moving along the x axis is given by

    x = 6.0t^{2} - 1.0t^{3} , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?


    2. Relevant equations

    motion equations and derivative/integration ideas from motion.

    3. The attempt at a solution
     
  2. jcsd
  3. Jul 17, 2008 #2

    Dick

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    You forgot to attempt a solution. Please try?
     
  4. Jul 17, 2008 #3
    How do you think you would get velocity from that expression?
     
  5. Jul 17, 2008 #4

    Dick

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    You are given position as a function of time. How is velocity related to position? I think you mentioned derivatives/integrals as things to use.
     
  6. Jul 17, 2008 #5
    ya i figured the derivative of position is velocity right, but I tried doing that and then using that as galileo's equation of motion, substituting the 12 and 3 for velocity and acceleration....but i kept getting numbers that didn't make sense.
     
  7. Jul 17, 2008 #6

    Dick

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    Yes, the derivative of the position is the velocity. Now how would you maximize it? Your description of what you did isn't very clear. Can you write it out completely, showing those numbers that 'don't make sense'?
     
  8. Jul 17, 2008 #7
    the derivative is 12t - 3t^(2). That is velocity, now to maximize the equation take the derivative of it??? and use that to plug into the other one?
     
  9. Jul 17, 2008 #8

    Dick

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    Yes, to maximize something you take it's derivative and set it equal to zero. In this case you are setting the acceleration equal to zero. At maximum velocity, the acceleration is zero.
     
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