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Position of a particle from the graph of its velocity

  1. Nov 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Problem: how do we know for sure if x is <0 for point A?
    AglX2zq.png
    Vx-t is a graph of particle's speed over time.
    x represents position of the particle at any given time

    3. The attempt at a solution
    From the function that we can see on the left side of the picture we can deduce the formula for it. It should be something like v = -a(t-b)^2+c, where a,b and c are some unknown constants >0.

    So i attempted to use wolframalpha to plot a function similar to this:
    LKtbnn1.png
    And then I took integral of this function to find the connection between x (position of the particle) and t:
    bsRhj1K.png
    From this function we can see that if the constant is equal to zero, then position x of the particle at t=0 should be zero. This means that since the textbook says that at point A x<0, our constant is =/=0, but instead is a negative number.

    But how do they know that constant is <0 at point A?
    All we have is a graph of the derivate of the function of particle's position (x) over time. When we take a derivative of this, the constant turns into zero, so I don't see the way that authors used to determine whether the constant is >0, <0 or 0. Why do they state that x<0 at A then if it could actually be anything?

    Thanks for help!
     
  2. jcsd
  3. Nov 8, 2015 #2

    PeroK

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    A graph of velocity against time does not imply an initial position. The book must have stated or assumed that ##x(t=0) < 0##.
     
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