# 1957 AHSME Problems/Problem 15

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The table below shows the distance $s$ in feet a ball rolls down an inclined plane in $t$ seconds.

$$\begin{tabular}{|c|c|c|c|c|c|c|}\hline t & 0 & 1 & 2 & 3 & 4 & 5\\ \hline s & 0 & 10 & 40 & 90 & 160 & 250\\ \hline\end{tabular}$$ The distance $s$ for $t = 2.5$ is:

$\textbf{(A)}\ 45\qquad \textbf{(B)}\ 62.5\qquad \textbf{(C)}\ 70\qquad \textbf{(D)}\ 75\qquad \textbf{(E)}\ 82.5$

## Solution

Looking at the pattern, we can determine that $t=10s^2$. Applying the relationship, we can see that $s = \boxed{\textbf{(B) }62.5}$ when $t=2.5$.