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# Why do we use a second order polynomial to fit our position versus time data?

- Why do we use a second order polynomial to fit our position versus time data? Please don't say because it looks good or fits the data. Give a physics-related explanation.
- Express your experimental value of g (acceleration due to gravity) using a 95% confidence interval and with correct significant figures.
- Does the true value of g=9.81 m/s2 lie within your range? The idea of a 95% confidence interval is that there is a 95% chance that the true mean lies within that range.
- Would you expect the data to fit a polynomial function as well if the ball was either much less dense or was allowed to fall for a longer time (and therefore much faster)? Please explain.
- Should the value of gravitational acceleration from your data depend on the time starting from zero or the ball starting from rest? Please explain carefully.