91Ó°ÊÓ

Determine the distance traveled for the following data: $$\begin{array}{l|llllllllll} t, \min & 1 & 2 & 3.25 & 4.5 & 6 & 7 & 8 & 9 & 9.5 & 10 \\ \hline v_{,} \mathrm{m} / \mathrm{s} & 5 & 6 & 5.5 & 7 & 8.5 & 8 & 6 & 7 & 7 & 5 \end{array}$$ (a) Use the trapezoidal rule, (b) the best combination of the trapezoidal and Simpson's rules, and (c) analytically integrating secondand third-order polynomials determined by regression.

A transportation engineering study requires that you determine the number of cars that pass through an intersection travelling during morning rush hour. You stand at the side of the road and count the number of cars that pass every 4 minutes at several times as tabulated below. Use the best numerical method to determine (a) the total number of cars that pass between 7: 30 and \(9: 15,\) and (b) the rate of cars going through the intersection per minute. (Hint: Be careful with units. $$\begin{array}{l|cccccc} \text { Time (hr) } & 7: 30 & 7: 45 & 8: 00 & 8: 15 & 8: 45 & 9: 15 \\ \hline \text { Rate (cars per 4 min) } & 18 & 24 & 26 & 20 & 18 & 9 \end{array}$$