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Particle moving along a parabola

  1. Sep 11, 2012 #1
    Can someone please check that everything I have done so far is correct?

    A particle movies along a parabola with the displacement equation s = 0.5t2.
    (a graph is shown)

    ::::Part I::::

    Suppose x-component is s = Ct
    i) indicate direction of velocity vector and acceleration at point R (arbitrary point on graph)
    ii) Determine y-component of particles velocity
    iii) Determine y-component of particles acceleration

    Answers:

    i) I suppose the velocity vector would be tangential to the graph and the acceleration vector would be parallel with the y-axis?
    ii) since V = √(Vx2 + Vy2), and V = t, I found that the y - component is √(t2-C2t2).
    iii) Since the acceleration is constant, is the y-component simply C?


    :::Part II::::


    Suppose instead that the x-component of the velocity is given by [tex]\frac{C}{\sqrt{1 + t^{2}}}[/tex]

    i) Show that the particle's speed is constant

    I am unsure how to attempt Part II.

    If you are able to answer or confirm my answers to any part of this question, thank you very much!
     
    Last edited: Sep 12, 2012
  2. jcsd
  3. Sep 12, 2012 #2
    Some help would be greatly appreciated!
     
  4. Sep 12, 2012 #3

    ehild

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    We need some explanation. What is s? I do not see the graph.

    ehild
     
  5. Sep 12, 2012 #4
  6. Sep 12, 2012 #5
    For part (i) - you are right,
    For part (ii) you have used s_x instead of V_x to determine V_y
    For part (iii) - yes, the acceleration is constant, but it is not equal to C; but maybe try determining the total acceleration, and the acceleration in the x direction instead of differentiating...
    - if you typo'd s=Ct; and it's actually V_x=Ct, then your answer to part (i) is wrong, part (ii) is right and you still need to determine part (iii) - it's a constant still, but not C

    For part (II)
    there isn't enoguh information - is the total motion of the particle still given by s=.5t^2?
    Because in that case, the particles speed can't be constant - it's speed is, as you said, is equal to t, which is a variable.
    Was there any other information?
     
  7. Sep 12, 2012 #6

    ehild

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    s=0.5t^2 is a scalar equation. If s is displacement, the particle moves along a straight line, not along a parabola. If a particle moves along a parabola, you need to give the relation between its coordinates. Can you show the original text of the problem?

    ehild
     
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