I avoid noise in the free fall data by having the students use 16
positions evenly spaced in time. The key point is that *no* position
gets used more than once. I ask them to calculate the average velocity
between the 1st and 9th point, the 2nd and 10th point, etc. to the 8 and
16th points. This means they only get 8 velocities, BUT THEY ARE
INDEPENDENT, AND ARE OVER LONG DISTANCES-SO SMALL POSITION ERRORS ARE'T
FATAL. I continue the pairing with the acceleration: the 1st and 5th
velocities give one average acceleration, the 2nd and 6th, 3rd and
seventh, 4th and eighth. They only get 4 accelerations, but all four
depend on widely separated position measurement, and are independent of
each other!