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Velocity and accleration of a particle

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data

    A particle moves along a curve whose equations are:
    x=3e^(-2t)
    y=4sin3t
    z=5cos3t
    where t is the time.
    a) Find the velocity and acceleration at any time.
    b) Find the magnitudes of the velocity and acceleration at time t=0.

    2. Relevant equations



    3. The attempt at a solution

    I know that the velocity is d/dt of the position and acceleration is d/dt of velocity. How can i find the velocity? If i take the derivative of all three functions, i will get three different velocities.
     
  2. jcsd
  3. Sep 18, 2007 #2

    Dick

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    How is the magnitude of a vector related to it's components?
     
  4. Sep 18, 2007 #3
    the magnitude is the square root of the components squared.
     
  5. Sep 18, 2007 #4

    Dick

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    Right! So apply that to the velocity and acceleration vectors to get the magnitude.The three different velocities and accelerations are components of vectors.
     
  6. Sep 18, 2007 #5
    so i find the velocities. then i have three different velocities, but i cant find the magnitude if i dont find velocity for a certain t.
    v(x)= -6e^(-2t)
    v(y)= 12cos3t
    v(z)=-15sin3t

    a(x)=12e^(-2t)
    a(y)=-36sin3t
    a(z)=-45cos3t

    now what...?
     
  7. Sep 18, 2007 #6

    Dick

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    Ordinarily, I would just say find the magnitudes as a function of t. But your problem says find them at t=0.
     
  8. Sep 18, 2007 #7
    well i can do part b with t=0. what about part a? i mean i have three different velocities and three different accelerations. for velocity, if i take the three components and square them then add them and find the square root, that gives the speed. its not a velocity at any time t. i'm assuming for part a, i need just one equation for velocity and one for acceleration.
     
  9. Sep 18, 2007 #8

    Dick

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    Your vector v above is the velocity at any time t. If you want a specific time then plug it in but if they say for ANY t, then that's the answer. Ditto for a.
     
  10. Sep 18, 2007 #9
    aren't there three vectors? three different equations for v? don't they want only one equation for velocity? and one for acceleration?
     
  11. Sep 18, 2007 #10

    Dick

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    No, there is one vector v(t)=(-6e^(-2t),12*cos(3t),-15sin(3t)). The vector has three components. You are done.
     
  12. Sep 18, 2007 #11
    Oh! Well i am done with this problem. Thanks for all the help, much appreciated.
     
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