What's a good way to explain dimensional analysis to a student?
Here's a simple question which this method would be useful:
Let's say a truck is moving with a speed of 18 m/s to a new speed of 13 m/s over a distance of 48 meters. How long did it take for the truck to break to its new speed, and what was the acceleration of the truck?
@TimGoodman and @Laar, Hmm. I was under the impression that you could solve such questions by analyzing their dimensional properties. For example, based on V1 and V0 in the example above I know the person decelerated 5m/s over a distance of 48 meters. If I want the time it took (first question) I can simply look at the units and see if I can eliminate all units except s (seconds). 48m/5m/s allows the meters to cancel out leaving 9.6 seconds.
Now I have a new peice of information and I can now solve the second question "What was the acceleration of the truck?" Since I'm solving for acceleration I know my final units will be m/s^2. I know the velocity of the deceleration was 5m/s and it took him 9.6s. Dividing 5m/s/9.6s = .52 m/s^2. My final units match and so by using dimensional analysis I've solved the problem.
Maybe I have a misunderstanding of dimensional analysis. Any suggestions?