this sounds like mathematician vs engineer.
you guys want the exact answer, we provide the best answer with the given information. yes the constant acceleration is an (false) approximation, but with a few more sampling points as suggested by djvapor you can construct a piecewise linear curve to integrate, or if you really wanted, use some higher order interpolation to construct a curve. Then you'll really start getting close without fancy shmancy equipement. sorry this post was unecessary i just dont like to get called wrong especially when i say what i did is based on assumption.
and yes, i am a math expert