Using and Converting Units
We use equations to express relationships among physical quantities, represented by algebraic symbols. Each algebraic symbol always denotes both a number and a unit. For example, d might represent a distance of 10 m, t a time of 5 s, and v a speed of 2 m>s.
An equation must always be dimensionally consistent. You can’t add apples and automobiles; two terms may be added or equated only if they have the same units. For example, if a body moving with constant speed v travels a distance d in a time t, these quantities are related by the equation
d = vt
If d is measured in meters, then the product vt must also be expressed in meters. Using the above numbers as an example, we may write
10 m = (2 m/s)(5s)
Because the unit s in the denominator of m>s cancels, the product has units of meters, as it must. In calculations, units are treated just like algebraic symbol with respect to multiplication and division.