A Physics Experiment Involving the Acceleration of Shuttle on a Rail

A physics experiment involving the acceleration of shuttle on a rail produced the following
data: $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | c | c | } \hline \text { Time (s) } & 0.017 & 0.05 & 0.083 & 0.117 & 0.15 & 0.183 & 0.217 & 0.25 & 0.283 & 0.317 & 0.35 & 0.383 \\\hline \text { Position (m) } & 0.020 & 0.046 & 0.081 & 0.129 & 0.187 & 0.256 & 0.337 & 0.427 & 0.529 & 0.640 & 0.765 & 0.899 \\\hline\end{array}$$ (a) Make a scatter plot of the data.(b) Fit a quadratic model to the data.(c) Based on your model, what was the initial position of the shuttle?
(d) Using your model, estimate the velocity of the shuttle when t = 0.1 and when t = 0.45 seconds.(e) What is your estimated acceleration of the shuttle when t = 0.1 and when t = 0.45 seconds?

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