Originally Posted by **W.D.Clinger**

The red line is NIST's linear approximation to part of NIST's nonlinear approximation.

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You were telling us that your [*acceleration*] polynomials must be better than NIST's [*acceleration*] approximations because (you thought) NIST's [*acceleration*] approximations were linear.

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you didn't realize that NIST's [*acceleration*] approximations were nonlinear

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NIST's model of the *acceleration *is not a straight line.

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NIST's models of displacement, velocity, and *acceleration *are all nonlinear.

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NIST's velocity and *acceleration *models are immediate consequences (via freshman calculus) of that nonlinear model.

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etc

Parentheses added by me for clarity of context.

A slight reminder on this point...

NIST only derived their displacement formula to velocity.

The only

*acceleration model* used is the

*linear regression*, and it is from that linear regression that their stated metrics are generated...

NIST used the datapoints circled in

red (which were themselves determined by

*central difference approximation* from the underlying displacement data) to calculate their stated linear regression (the

red line)...

*v(t) = -44.773 + 32.196t *
It is this linear regression which is used to specify the rough 2.25s *freefall* period.

That fact is made even clearer if we actually look at the implied NIST acceleration function (which they did not use) and check the period of time which it can reasonably be said to approximate gravitational acceleration...

I have taken the liberty of marking a 2.25s duration in

red and gravitational acceleration in

cyan.