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Finding time.

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data

    A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. On seeing the meter stick released, you grab it with these two fingers. You can calculate your reaction time from the distance the meter stick falls, read directly from the point where your fingers grabbed it. If the measured distance is 17.6cm , what is the reaction time?

    So I googled it and it said t=√d/4.9m/s^2
    How is that derived?



    2. Relevant equations

    v2=v1+at
    x=v1t+1/2at^2
    x=1/2(v1+v2)t
    v2^2=v1^2+2ax

    3. The attempt at a solution
    I converted 17.6cm to 0.0176m. Now my question is how would I approach this kind of question without all the given variables?
    This is my attempt at it.
    x=0.176m
    a=-9.8m/s^2
    0.176=v1t+1/2(-9.8m/s^2)t^2
    0=-0.176+v1t+(-4.9m/s^2)t^2
    but now I don't have a variable for v1 how to solve for v1
     
    Last edited: Jan 27, 2013
  2. jcsd
  3. Jan 27, 2013 #2
    v1 is the initial velocity. Initially, the meterstick is at rest. Therefore v1 = 0.
     
  4. Jan 27, 2013 #3

    Doc Al

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    Staff: Mentor

    v1 is the initial velocity of the falling object.
     
  5. Jan 27, 2013 #4
    So if v1=0 then i could use x=v1t+1/2at^2...
    0.176=1/2(-9.8m/s^20)t^2 then solve for t^2
    t^2=0.176m/(-4.9m/s^2) but it wouldn't work because I cant square a negative or do i have to use the positive 4.9m/s^2
     
  6. Jan 27, 2013 #5
    You have to make sure your signs are consistent.
    Why are you choosing the displacement (x) to be positive but the acceleration (a) to be negative? In this situation, they should be in the same direction (downward).
     
  7. Jan 27, 2013 #6
    Well, the expression really is x - x0 = v0*t + 0.5*g*t^2.

    Now the signs will depend on the choice of the x axis direction. If it points downwards you will assume x = d and x0 = 0 and g = 9.8 (because the gravity pull is in the positive x-axis direction); if you choose an x-axis pointing upwards then x = -d and x0 = 0 and g = -9.8 because the pull is opposite to the positive direction). In each case you get the same answer and there is no negative root to concern yourself with.
     
  8. Jan 27, 2013 #7
    Thanks @rikardus !! How did you come up with that expression? did you made
    Δx = (v1)t+1/2(a)t^2
     
  9. Jan 27, 2013 #8
    Yes I did. I'm also used to the v0 notation to emphasize that is an initial velocity.

    You're welcome.
     
  10. Jan 27, 2013 #9
    Okay cool and I figured, that's how it is my book but for some reason my professor uses v1 and v2
     
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