Using velocity and acceleration vectors to interpret the motion of a car

This activity is designed for students to better understand the vector nature of velocity and acceleration and to predict the motion of a vehicle in terms of its velocity and acceleration.
Lesson Concepts:
1) Velocity and acceleration are vector quantities (quantities with magnitude and direction components).
2) Acceleration refers to increasing speed, decreasing speed, and/or changing direction.
Lesson Vocabulary:
1) vector
2) velocity
3) acceleration

I envision this activity to be a supplement to the motion chapter (chapter 9) in Prentice Hall's Science Explorer Physical Science textbook. The students should have already explored the terms of speed, velocity, and acceleration; the term vector will be introduced through this lesson. This lesson is a combination of lecture/note-taking and hands-on manipulation of physical models of vectors. Materials include wood toothpicks or skewers, markers, and an overhead projector/white board/etc.

- class discussion/notes –
1) Introduce the term vector (a quantity with both magnitude and direction); velocity and acceleration are both vector quantities.
2) Draw a race track with both straight and curved portions; pick various points on the track to investigate; for each point, label its velocity and draw the acceleration vector related to that velocity vector required to keep the car on the race track.
3) Replace the drawn vectors with two toothpicks/skewers (each with a different colored tip to designate direction of the vector); demonstrate that the arrangement of these two vectors (velocity and acceleration) will determine the motion of a car.
4) Further practice for the students: remove the race track diagram; toss toothpicks into the air; once they've landed on overhead projector/desk, ask students to predict the motion of the car; discuss as class.

- hands-on manipulation of vectors -
5) Students should break out in groups of two or three; each group will be given a set of toothpicks and a set of note cards. These note cards will have various car motions printed on them (e.g. speeding up and going straight, slowing down and going straight, turning to the right at a constant speed, turning to the left and slowing down, etc.). Groups should arrange their toothpicks in the correct formation to match the card's description. They will check-in with the instructor to see if correct before moving onto the next note card.
6) Then groups should toss toothpicks onto their desks/work stations and describe the motion of the car based on this vector arrangement. Students should repeat this portion 3-5 times, making sure each student in the group has a turn to toss their vectors.
This activity is a modification from the "Motion in Two Dimensions" investigation performed at the Secondary Physics MnSTEP Institute, July 2009. Sample vector diagrams (Microsoft Word 27kB Jul22 09)

I have not yet done this activity with my middle school students; I foresee a few areas of confusion and concern. Logistically, it will take time for the instructor to check in with every group during the note-card portion of the activity; it might be helpful to have the students work on a related motion worksheet/project during any down time while they're waiting for the teacher. Students may also need much practice with the concept of the acceleration vector; for example, even though the acceleration vector might be pointing to the right, it does not necessarily mean the car will be traveling in that direction. The car's motion all depends on the arrangement of both the velocity and acceleration.

In addition to on-going observation throughout the activity, I will require the students to interpret various velocity-acceleration vectors on a worksheet which they will turn in.

Standards Match:
6.2.2.1.1 – speed
6.2.2.2.1 – forces