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

by seasnake
Tags: acceration, algebraic, intra-interval, rate
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Jun20-09, 12:33 PM
P: 42
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.
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Jun20-09, 12:58 PM
Sci Advisor
HW Helper
P: 4,300
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)
Jun20-09, 04:14 PM
Sci Advisor
PF Gold
P: 39,490
Since this is not "Linear and Abstract Algebra", I am moving it to "General Math".

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