Shakespeare once wrote that "a rose by any other name would smell as sweet". In physics we would say that "a concept labeled by any other tag will still have the same meaning".
In all but the simplest problems, it will be necessary for you to generate your own personal labels to tag the information given and requested. Your personal labels for the variables involved will not necessarily be the same as those in the generic equations in the textbook.
Example:
Train A leaves town A at the same time as train B leaves town B. Train A travels at a constant speed of 45.0 km/hr towards town B, and train B travels at a constant speed of 63.0 km/hr towards town A on parallel tracks. If the towns are 120 km apart, how long (after they start) will the trains pass ?
This problems involves only constant motion, so the generic equation that applies is x = v t . Here we assume the trains start from rest and we can neglect the time it took the trains to start their motion.
Look at the solution if we only used generic variables for the equation associated with constant motion.
Solution: When the trains meet, the total distance they will have traveled will be equal to the distance between the two towns.
You may be able to understand this solution, since it only involves a few variables and it is possible to keep track of the meaning of these variables by the context in which they appear. However, as problems become more complex, this becomes harder and harder to accomplish since most people can only keep track of about seven things in their mind at one time. Moreover, the above solution is mathematically incorrect since v + v = 2 v.
Compare This solution with the following in which personal labels are used.
Given:
| d = 120 m | Distance between the towns | |
| vA = 45.0 km/hr | Speed of train A | |
| vB = 63.0 km/hr | Speed of train B | |
| tp = ? | Time when trains pass | |
| dA = ? | Distance traveled by train A | |
| dB = ? | Distance traveled by train B |
Solution: When the trains meet, the total distance they will have traveled will be equal to the distance between the two towns.
This solution is a lot longer but is also a lot clearer. If I were solving the problem I would probably not bother to spell out the meaning of every variable, but would keep "in mind" the meaning of the subscripts. Subscript A labels the variables associated with train A and subscript B labels the variables associated with train B. I would have also drawn a sketch in which I would keep track of the meaning of my personal labels by their location on the sketch.
