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Formula help needed algebraic formula for intra-interval rate of acceleration

  1. Jun 20, 2009 #1
    This isn't for a class, just for my own personal use as I am not a student, but I need an equation in algebraic form that allows me to calculate the average acceleration between spreadsheet intervals given that the intra-interval rate of acceleration is to be treated as a constant, and the speed at the beginning of the interval is known and the speed at the end of the interval is also known.

    T = time
    Speed at T = 4 is 6
    Speed at T = 5 is 4
    Speed at T = 6 is 7
    Speed at T = 7 is 7

    I am searching for an algebraic formula (non-derivitative, non-trig) that gives the average rate of intra-interval acceleration if the rate of intra-interval acceleration were constant between T = 5 and T = 6. Speed at T = 4 and speed at T =7 should have no impact to this intra-interval multiplier.

    Said another way, I have a spreadsheet and I have formulated it so that the average rate of interval acceleration between T = 5 and T = 6 is (Speed at T = 5 + Speed at T = 6)/2, but I know that this is incorrect as the intra-interval rate should rise exponentially between T = 5 and T = 6, so instead of multiplying by 0.5 I should be multiplying by a different fraction that is exponentially related.
    Last edited: Jun 20, 2009
  2. jcsd
  3. Jun 20, 2009 #2


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    Homework Helper

    Acceleration is change of speed per time step, not average velocity during the time step.
    So the acceleration between time T and T' is
    [(speed at T') - (speed at T)] / (T' - T)
  4. Jun 20, 2009 #3


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    Science Advisor

    Since this is not "Linear and Abstract Algebra", I am moving it to "General Math".
    Last edited by a moderator: Jun 20, 2009
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