Stopping distances The table lists the practical stopping...

Stopping distances The table lists the practical stopping distances $D$ (in feet) for cars at speeds $S$ (in miles per hour) on level surfaces, as used by the American Association of State Highway and Transportation Officials. $$\begin{array}{|c|rccccc|} \hline \boldsymbol{S} & 20 & 30 & 40 & 50 & 60 & 70 \\ \hline \boldsymbol{D} & 33 & 86 & 167 & 278 & 414 & 593 \\ \hline \end{array}$$ (a) Plot the data. (b) Determine whether stopping distance is a linear function of speed. (c) Discuss the practical implications of these data for safely driving a car.

Stopping distances The table lists the practical stopping distances $D$ (in feet) for cars at speeds $S$ (in miles per hour) on level surfaces, as used by the American Association of State Highway and Transportation Officials.
$$\begin{array}{|c|rccccc|}
\hline \boldsymbol{S} & 20 & 30 & 40 & 50 & 60 & 70 \\
\hline \boldsymbol{D} & 33 & 86 & 167 & 278 & 414 & 593 \\
\hline
\end{array}$$
(a) Plot the data.
(b) Determine whether stopping distance is a linear function of speed.
(c) Discuss the practical implications of these data for safely driving a car.

Key Concepts

Nonlinear Relationships

Nonlinear relationships occur when the change between variables is not constant, and the graph of the data forms a curve rather than a straight line. Recognizing nonlinearity is important because it indicates that factors influencing the variables have a more complex interaction, which may require different analytical approaches for accurate modeling.

Practical Implications in Safety and Driving

Understanding the relationship between variables such as speed and stopping distance has practical implications for road safety. Analyzing these relationships helps in setting appropriate speed limits, designing safer traffic systems, and informing drivers about the increased risks associated with higher speeds, ultimately contributing to more informed and safer driving practices.

Linear Functions

A linear function describes a relationship between two variables where the change in one variable is directly proportional to the change in the other, resulting in a straight-line graph. Evaluating whether data follow a linear pattern involves checking if the increments between values are consistent, which is critical for modeling and prediction in many contexts.

Data Visualization

Data visualization is the graphical representation of information and data. It involves plotting data points on a chart or graph to identify patterns, trends, and relationships, making it easier to interpret numerical information visually. This process is essential in transforming raw data into a format that can be quickly comprehended and analyzed.

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