# Motion Concepts: Displacement, velocity, & acceleration graphs

### This activity has benefited from input through a review and suggestion process.

This activity has benefited from input from faculty educators beyond the author through a review and suggestion process as a part of an activity development workshop. Workshop participants were provided with a set of criteria against which they evaluated each others' activities. For information about the criteria used for this review, see http://serc.carleton.edu/sp/compadre/devactivities/reviewcriteria.html.

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

Students often struggle with motion concepts. These activities focus on the graphical representations of displacement, velocity, and acceleration given a number of situations of an object moving along the x-axis.

These activities are based upon asking students to determine appropriate graphical representations in a variety of settings. After an initial vote (via clickers, raising hands, etc), students should pair up and discuss before re-voting. The PhET simulation "The Moving Man," downloadable for free at http://phet.colorado.edu/web-pages/simulations-base.html, allows the instructor to setup the situation and have real-time graphs displayed as the man moves. Therefore, concepts can be demonstrated in a variety of settings during class-time. These activities are appropriate before or after similar investigations in the laboratory for all levels of students investigating motion.

## Learning Goals

The goal of this activity is to promote proper conceptual understanding of motion, especially as motion is shown via position versus time, velocity versus time, and acceleration versus time graphs. Students should learn how these three types of graphs (position, velocity, and acceleration versus time) are all directly related. Students will be able to draw appropriate motion graphs for a variety of types of motion as well as describe the motion displayed in a variety of motion graphs.

## Context for Use

These questions are to be used for in-class peer instruction. Students should make predictions, share predictions, and discuss and make a new prediction. There should also be a general class discussion/presentation after each question to clarify the material. These activities are appropriate in a variety of settings as described below:

Educational level: Conceptual physics to calculus-based physics

Setting: These concept tests can be used as a pre-lab, post-lab, or classroom activity; The activities are appropriate for small classes to large lecture hall classes.

Time required: Instructors may stream-line or expand these activities. A minimum time of 15 minutes should be allotted for these activities.

Special equipment: computer & LCD projector (note PhET does not require internet access)

Pre-requisite knowledge: Students should have had an introduction to the slope of a line, reading graphs, and motion terminology (position, displacement, velocity, & acceleration).

## Description and Teaching Materials

The simulation integrated with the concept test questions allows the instructor to immediately follow up each concept test with a demonstration that includes the ability to change a variety of aspects of the Moving Man's motion all while the real-time position, velocity, and acceleration graphs are shown. The initial conditions (position, velocity, and acceleration) can be changed within the simulation.

The virtual experiment can be done with the PhET Circuit Simulator from the University of Colorado. This is available at

Instructions on the PhET activities can be found at the websites mentioned above. The concept test questions are designed to engage students but also to allow both students and instructor to gauge understanding about motion. The concept test questions are presented within a Power Point file. Instructors may choose to add questions as time allows. (PowerPoint 199kB Jul29 07)

## Teaching Notes and Tips

Students must become engaged in the class/lab activity in order for us to help them learn. Students should commit to an answer before the demonstration, either by written responses or some manner of class-room voting (classroom response, raised hands, etc). Peer Instruction, where students can learn from each other before re-voting, has proven to be an effective tool for engaging students. The PhET "moving man" can be used initially to demonstrate, in real-time, the graphs resulting from different types of motion (e.g. constant velocity, negative velocity with positive acceleration, etc). If during the concept-test questions, students demonstrate misconceptions, the instructor may want to perform additional "moving man" simulations.

## Assessment

Similar multiple choice questions can be asked in homework, quiz, or test assessments. In addition, students may be asked to draw the position, velocity, and / or acceleration graphs for an instructor described situation. Alternatively, given position, velocity, and acceleration versus time graphs, the students may be asked to describe (predict) the motion of the object as part of assessment activities.

## References and Resources

Results of studies on the effectiveness of PhET simulations, and presentations given about the PhET materials are available at http://www.colorado.edu/physics/phet/web-pages/research.html .