There is a second rule that we need to apply to an algebraic treatment of quantities. In this equation, the acceleration, a, has the dimensions length x time -2 while t 2 has the dimensions time 2 . This is the same dimension as the distance s on the left hand side. By adopting this convention we ensure that all the equations we write are unit-neutral. It cannot be emphasized too strongly that this convention can never be taken for granted.
Textbooks contain numerous examples of equations which are unit-dependent.
In other words, these equations only work for a specific set of units. Moreover, if we include the units they do not cancel correctly. The symbol t represents the number of seconds while the symbol s represents the number of feet . In the first place we need to carefully spell out which units are intended. Here again t stands for a pure number, namely the number of seconds, while s represent the number of meters .