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

  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. CompuChip

    CompuChip 4,297
    Science Advisor
    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. HallsofIvy

    HallsofIvy 40,767
    Staff Emeritus
    Science Advisor

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