Whether at the high school or middle school level, students studying graphs of motion are often confused. One area of confusion occurs in the difference between distance-time graphs and displacement-time graphs. Virtual activities can cause more confusion, unless the right ones are chosen.

Distance-time graphs are a part of many middle school math and science curricula. A Google search for “distance-time graphs” reveals about 10,500 websites with many Java-based and Flash-based online activities. The problem for physics learners and teachers is that in many cases, the developers call their graph a distance-time graph but in reality they are displacement-time graphs.

Here are some examples of (otherwise) good websites making this error:

Moving Man 

Football (soccer) Distance Time Graph

GCSE Bitesize 

There are a few good sites that accurately portray distance-time graphs.

“Crocodile-clips” is a simple, free site where students move a helicopter and create a real-time distance-time graph. It doesn’t matter if the helicopter is moved away from or closer to the starting point. The true distance traveled is displayed on the graph. It is simple but effective.

Commonwealth Curriculum Pack (CCP) is a more involved site. I used this with my mixed age physics class last week and it made the point and kept their interest.

This site uses the context of the 100-meter race to show different arrival speeds. Quickly, my students learned that the steeper the slope (gradient), the greater the speed of the runner. Then we viewed several nice animated sequences of interpolation, which they then interpreted.

PBS Teacher Line http://www.pbs.org/teacherline/resources/activities/race/readings/race.htm.

Students observe stick figures run 400-meter races. They can see the runners move at actual speeds or average speeds, so this serves as a good way to help students understand instantaneous speed versus average speed.

Motion graphs will probably always be confusing for some students. We can reduce confusion with distance-time and displacement-time graphs by using internet resources that accurately portray the difference.

Additional Resources

Adaptive Curriculum’s Activity Object: “Truck On: Position and Velocity-Time Graphs” 

The Physics Classroom Tutorial: Distance and Displacement