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Look of trajectory of a material point

  1. Oct 8, 2014 #1
    1. The problem statement, all variables and given/known data
    A body is moving, with the following data (these are all dependencies of the radius vector components respective to time): x(t)=At2, A>0; y(t)=Bt, B>0, z(t)=0. How does the trajectory of this movement look?

    2. Relevant equations
    r=x(t)i+y(t)j+z(t)k
    Velocity=dr/dt
    3. The attempt at a solution
    r=At2*i+Bt*j (i,j and r are vectors)
    Velocity=2At*i+B*j
    Intuitively I think that the trajectory would look like a logarithm function, but is it correct and how to prove it?
     
  2. jcsd
  3. Oct 8, 2014 #2

    gneill

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    Staff: Mentor

    Since z(t)=0 for all t the trajectory must lie entirely in the x-y plane. Did you try to sketch the trajectory? Pick arbitrary values for A and B and plot a few points. Alternatively, find y as a function of x and comment on the type of function it represents.
     
  4. Oct 8, 2014 #3
    You may know already a type of motion which satisfies similar conditions.
     
  5. Oct 8, 2014 #4
    I thought that it would look similar to y=log(x). Correct?
     
  6. Oct 8, 2014 #5

    gneill

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    Staff: Mentor

    Similar it may be, but you can find the actual equation by converting from parametric form to standard y(x) = ... form.
     
  7. Oct 8, 2014 #6
    Is it y=B*sqrt(x/A)?
     
  8. Oct 8, 2014 #7

    gneill

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    Staff: Mentor

    Yup. Or if you combine the constants, ##y = c\sqrt{x}## .
     
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