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 \equal{} 2.5$ is:

$ \textbf{(A)}\  45\qquad 
\textbf{(B)}\ 62.5\qquad 
\textbf{(C)}\ 70\qquad 
\textbf{(D)}\ 75\qquad 
\textbf{(E)}\ 82.5$
1. **Identify the pattern in the given data:**
   The table shows the distance \( s \) in feet a ball rolls down an inclined plane in \( t \) seconds. We need to find a function that fits the given data points.

   \[
   \begin{array}{|c|c|c|c|c|c|c|}
   \hline
   t & 0 & 1 & 2 & 3 & 4 & 5 \\
   \hline
   s & 0 & 10 & 40 & 90 & 160 & 250 \\
   \hline
   \end{array}
   \]

2. **Determine the relationship between \( t \) and \( s \):**
   We observe that the distance \( s \) seems to follow a quadratic relationship with \( t \). Let's assume \( s = k t^2 \) for some constant \( k \).

3. **Find the constant \( k \):**
   Using the data point \( (t, s) = (1, 10) \):
   \[
   10 = k \cdot 1^2 \implies k = 10
   \]

4. **Verify the relationship with other data points:**
   - For \( t = 2 \):
     \[
     s = 10 \cdot 2^2 = 10 \cdot 4 = 40
     \]
   - For \( t = 3 \):
     \[
     s = 10 \cdot 3^2 = 10 \cdot 9 = 90
     \]
   - For \( t = 4 \):
     \[
     s = 10 \cdot 4^2 = 10 \cdot 16 = 160
     \]
   - For \( t = 5 \):
     \[
     s = 10 \cdot 5^2 = 10 \cdot 25 = 250
     \]

   The relationship \( s = 10 t^2 \) holds for all given data points.

5. **Calculate \( s \) for \( t = 2.5 \):**
   \[
   s = 10 \cdot (2.5)^2 = 10 \cdot 6.25 = 62.5
   \]

Conclusion:
\[
\boxed{62.5}
\]