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Mechanics, Distance and speed question

  1. Mar 31, 2016 #1
    What is the relationship between the distance y travelled by an object falling freely from rest and the time x the object has been falling?

    The answer to this question is: y is proportional to x2

    Can someone tell me how this answer is correct.
     
  2. jcsd
  3. Mar 31, 2016 #2

    Doc Al

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    Staff: Mentor

    Are you familiar with the kinematics of falling bodies? (An example of constant acceleration motion.)
     
  4. Mar 31, 2016 #3
    Yes, I understand that but I still do not understand why it is X^2. Can you please explain and thank you.
     
  5. Mar 31, 2016 #4

    Doc Al

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    They are just using, for some strange reason, "X" to stand for the time. Is that the concern?

    Can you write the kinematic equation for distance as a function of time?
     
  6. Mar 31, 2016 #5
    s=ut+at^2/2 and s=(u+v)/2 x t there is a lot more
     
  7. Mar 31, 2016 #6

    Doc Al

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    That's the one you need. Since the object is falling from rest, what is u? And change the standard variable names to what they want in the problem, Y and X.
     
  8. Mar 31, 2016 #7
    Thank you indeed but last question: why do we reject the other equations.
    and also even if I make the initial velocity zero, then I would end up with 2s=at^2, t
     
  9. Mar 31, 2016 #8

    Doc Al

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    Only because we want an equation that links distance to time. The other equations link other variables, so they won't help us here.

    Sure, you end up with s=at^2/2 = (a/2)t^2.

    Which tells you that the distance fallen is proportional to the square of the time. (You can replace s with y, and t with x, to make it match the variable names used in the problem statement.)
     
  10. Mar 31, 2016 #9
    Thank you very much, great mentor!
     
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