written by
Gary Gladding
published by
the University of llinois Physics Education Research Group

This interactive homework problem involves distance and deceleration in the context of a speeding driver who brakes to avoid being caught by the highway patrol. Given the initial speed of the car and rate of deceleration, how far away was the patrol car when the driver spotted it?

The problem is accompanied by a sequence of questions designed to encourage critical thinking and conceptual analysis. It is part of a larger collection of interactive problems developed by the Illinois Physics Education Research Group.

Editor's Note:This problem gives students practice in using the area under the curve on the Velocity vs. Time graph to calculate distance. It provides comprehensive support and immediate feedback at every step to help learners graph the motion and analyze how to solve the problem.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

12. Habits of Mind

12B. Computation and Estimation

9-12: 12B/H1. Use appropriate ratios and proportions, including constant rates, when needed to make calculations for solving real-world problems.

9-12: 12B/H2. Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable.

9-12: 12B/H3. Make up and write out simple algorithms for solving real-world problems that take several steps.

Common Core State Standards for Mathematics Alignments

High School — Number and Quantity (9-12)

Quantities^{?} (9-12)

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

High School — Geometry (9-12)

Expressing Geometric Properties with Equations (9-12)

G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.^{?}

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=6483">Gladding, Gary. Illinois PER Interactive Examples: Highway Patrol. Urbana: University of llinois Physics Education Research Group, September 2, 2006.</a>

G. Gladding, (University of llinois Physics Education Research Group, Urbana, 2002), WWW Document, (https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol).

G. Gladding, Illinois PER Interactive Examples: Highway Patrol, (University of llinois Physics Education Research Group, Urbana, 2002), <https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol>.

Gladding, G. (2006, September 2). Illinois PER Interactive Examples: Highway Patrol. Retrieved January 23, 2021, from University of llinois Physics Education Research Group: https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol

Gladding, Gary. Illinois PER Interactive Examples: Highway Patrol. Urbana: University of llinois Physics Education Research Group, September 2, 2006. https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol (accessed 23 January 2021).

%A Gary Gladding %T Illinois PER Interactive Examples: Highway Patrol %D September 2, 2006 %I University of llinois Physics Education Research Group %C Urbana %U https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol %O text/html

%0 Electronic Source %A Gladding, Gary %D September 2, 2006 %T Illinois PER Interactive Examples: Highway Patrol %I University of llinois Physics Education Research Group %V 2021 %N 23 January 2021 %8 September 2, 2006 %9 text/html %U https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/01/IE_highway_patrol

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