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Straight-line graph

  1. Apr 15, 2005 #1
    A stone slides across an icy surface and travels a distance of x in time t while suffering uniform retardation. Which of the following pairs of quantities, plotted to represent the motion of the stone, would give a straight-line graph?

    A. x and t
    B. x and t2
    C. x/t and t2
    D. x/t and t
    E. x/t2 and t

    This is my approach to the problem:

    The initial velocity, u = at.

    Hence, the distance travelled by the stone, x = 0.5at2

    x/t2 = (0.5at2)/t2

    = 0.5a

    Since a is a constant, then a flat line would be represented in a graph of axes x/t2 and t.

    Also, in D., x/t = v, which decreases at a constant rate because of the constant deceleration, so this is another straight-line graph.

    Obviously, there must be something wrong with my reasoning because there can only be one, and not two answers for each multiple choice question.
     
  2. jcsd
  3. Apr 15, 2005 #2

    SpaceTiger

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    Are you sure that's the full equation for position as a function of time? What about the initial velocity?
     
  4. Apr 15, 2005 #3
    x = at(t) + 0.5 at2
    = 1.5 at2 ???

    This does not seem right.
     
  5. Apr 15, 2005 #4

    SpaceTiger

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    Have you ever seen the formula:

    [tex]x=v_0t+\frac{1}{2}at^2[/tex]
     
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