The Speed of a Runner Increased Steadily During the First

The speed of a runner increased steadily during the first three seconds of a race.Her speed at half-second intervals is given in the table.Find a lower estimate for the distance that she traveled
during these three seconds. $$\begin{array} { | c | c | c | c | c | c | c | c | } \hline t ( \mathrm {~s} ) & 0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 \\\hline ( \mathrm { f } / \mathrm { s } ) & 0 & 2.1 & 5 & 6.8 & 9.7 & 12.9 & 17.5 \\\hline\end{array}$$

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