Introduction
"A Bad Day for Sandy Dayton" was written to introduce general education, non-science majors to the concepts of motion, force and mechanical energy in a problem-based learning format. I chose to create the scenario of a rear-end car crash just outside the Physics Building where class was held. The intersection was easily accessible for taking measurements and timing the traffic light as we worked through the problem, and the location made the problem realistic for students.

I teach this course to one hundred and twenty students in a fixed seat auditorium. The students meet in the large class twice weekly for seventy-five minutes, then meet with their graduate teaching assistants one hour weekly for discussion, and two hours weekly for lab. The problem drives instruction in all three, where students in their permanent groups of four are challenged to learn the concepts of velocity, acceleration, Newton's First and Second Laws, and kinetic energy by working through the concepts related to the problem experimentally in lab, and by sharing information and research in the large class and discussion.

I introduced the first page of the problem on the second day of the semester, and cycled in and out of the four-part problem for five weeks as students researched the learning issues related to the problem. Because many of the students in this course are weak in math skills, I chose to have students interpret graphs to find stopping distances of vehicles rather than use algebraic formulas. This problem could be adapted for use in an algebra-based physics course, by having students work formally through the mathematics involved. As I comment on how I used each page of the problem, I will make reference to how the problem could be used in higher level courses.

Major Issues
Part 1 of the problem introduces students to the concept of speed (graphically and algebraically), forces on objects traveling at constant speed, and reaction time. As students explore these topics in class, they look at a variety of representations of motion, learn to interpret graphs of motion, and sketch graphs from data they derive experimentally, or from strobe photos. Newton's First Law is discussed as they begin to look at the effect of forces on motion. Students find their own reaction time (by catching a dropped ruler and interpreting a graph of "Dropped Distance" vs. "Time" (see graph 1)) and discuss variables that would affect that time.

The first two questions on page one are designed initiate student discussion about the concepts addressed in the unit: motion and forces. Most of us have experience with car accidents, either personally, through family or friends, or through TV and the movies. Students generally bring up questions such as the following:

• "What were the speeds of the car and van?"
• "How close was the van to the car?"
• "What was the speed limit?"
• "Where did the car and van end up?"
• "Were there witnesses?"

Students also mention measuring skid marks, finding the weight of the car and van, testing drivers for drugs and alcohol.

In question three and four, I cycled out of the problem to introduce the concept of speed, and begin students discussing various ways of representing motion using strobe photos, and simulators. Students gathered their own data in lab and graphed it. Forces are introduced at this point, with students understanding that when objects move at a constant speed, the forces on the object are balanced. Newton's First Law is also introduced at this point in the problem.

In answering questions five and six students recognize that drinking, drugs, speed of the car, condition of the road, lack of sleep, talking on the cell phone, and a variety of other factors affect a driver's reaction time.

Part 2 motivates students to explore the safety issues of seatbelts and airbags, how they work, and what happens if they are not used. Newton's First Law is revisited when students learn about "three collisions in a collision" while answering the first and second question. The "first collision" refers to the impact that the car makes with some other object (such as another car, a wall, or a tree). Once the vehicle stops, the people (and other objects) in the car continue to move at the initial speed of the car until they are brought to a stop by an object (such as the steering wheel, windshield, seatbelt). In the "third collision", the internal organs (heart, lungs, brain) in the body will continue to move at the speed of the car until they are stopped by the frame of the body. The "third collision" is the deadliest.

In answering question one, students will assume that Sandy will be getting X-rays for neck injury. This is a good time to describe the "three collisions in a collision" since the EKG will be checking for heart damage. Before answering question number three, I show crash dummy collisions on video and then ask students to analyze the collision in terms of forces on the car and person. This is a good time to remind students of Newton's First Law. You may want to have students research safety issues such as seatbelts and airbags, understand how they work, and how they minimize the forces on the body in a collision.

Part 3 asks students to sift through information in an accident report in order to separate fact from conjecture. They also explore the relationship of the speed of a vehicle to its stopping distance, and factors that affect the ability of a car to stop. They analyze the intersection in question, measuring the width of the intersection, the timing of the yellow light, the speed limit to determine whether the intersection is safe (see Eisenkraft, A.(1998) Active Physics: Transportation It's about Time, Inc. Armonk, NY.). Since these students are non-science majors, I have them analyze graphs of Stopping Distance vs. Initial Velocity (see Graph 2) for specific deceleration rates (or coefficients of friction) rather than have them analyze this mathematically. The graphical interpretation seems to make this analysis more accessible to them. In a higher level physics class, students could analyze the frictional forces involved and calculate the initial velocity prior to braking.

In Part 4 the students are given more information to use in doing a final reconstruction of the accident. They use the Stopping Distance VS Initial Velocity graphs to find Sandy's and Jerry's speed prior to braking. They use an average reaction time (between one and two seconds) to determine how far the vehicle traveled while the driver was reacting. Since I did not introduce Conservation of Momentum in this course, I gave students the information they needed to determine the speed that Jerry's van decreased during impact. In a higher level course, students would be expected to work through that analysis on their own.

Most students are able to recognize that Sandy and Jerry were both driving over the speed limit, and that Jerry was following to closely to Sandy's car.

After the problem is finished, I introduce kinetic energy and energy transformations. Students, in their groups, analyze the transformation of energy in car crashes by recognizing that moving objects have kinetic energy. Since the car and van have no kinetic energy after they come to rest after the impact, student explore the question, "Where did the energy go?" They look at the heat energy produced by the frictional forces in braking and skidding, as well as the energy used to produce sound, the energy used in deforming materials, and the kinetic energy of the pieces of the vehicles that fly off in different directions.

Classroom Management
Each page of the problem sets the stage for students to explore and research the concepts connected to that part of the problem. Students in their groups discussed the answers to the questions on each page, and also listed their own questions (or learning issues). In a general class discussion, all the learning issues from the groups were listed on an overhead. Those learning issues drove instruction in the next class. For example on the first page, one group may ask how you can represent the speed of an object. That question directs the teacher to explore the various ways to graphically represent motion, asking students to graph the motion of an object going at constant speed, constantly increasing speed, or constantly decreasing speed.

During the five-week unit, the class cycled through group discussion, general class mini-lecture, class discussion, independent research, and introduction to a new page in the problem.