Chapter 4, Problem 14PS

(a)

To determine

To calculate: The quadratic regression model for the provided data after converting the speed into metres per second; $\begin{array}{cccccc}v& 20& 40& 60& 80& 100\\ d& 5.1& 13.7& 27.2& 44.2& 66.4\end{array}$

(b)

To determine

To prove: The difference in times when the vehicles passed a certain point is $T=\frac{d\left(s\right)}{s}+\frac{5.5}{s}$.

(c)

To determine

To calculate: The speed that minimizes the time between the vehicles where $d\left(s\right)=0.071s^2+0.389s+0.727$

(d)

To determine

To calculate: The speed in kilometres per hour that minimizes the time between the vehicles and the minimum value of the time where $d\left(s\right)=0.071s^2+0.389s+0.727$

(e)

To determine

To calculate: The optimal distance between two vehicles if $d\left(s\right)=0.071s^2+0.389s+0.727$.