With the introduction of motion, there are now several dimensions that could appear in any problem. For example, a question may give change in position of 5m and a change in time of 5s and ask for the average velocity. If a velocity is the desired answer, the answer must have units of distance/time. It is then immediately obvious that an answer erroneously found by multiplying Ds by t must be incorrect because this answer has units of m•s instead of m/s. The correct method of dividing Ds by t gives units of m/s, a good check that the correct method of problem solving has been used.
