A physical quantity is a property of a material, substance or system which can be measured/quantified. Examples include the mass of a ball and the volume of a gas.
Fundamental quantities/Base quantities
These are the physical quantities from which all other physical quantities are derived. According to the International System of Units (SI), there are seven (7) fundamental quantities:
| Quantity | Symbol | Unit | Abbreviation for unit |
|---|---|---|---|
| Mass | $m$ | kilogram | $kg$ |
| Length | $l$ | metre | $m$ |
| Time | $t$ | second | $s$ |
| Temperature | $T$ | Kelvin | $K$ |
| Amount of substance | $n$ | mole | $mol$ |
| Current | $I$ | ampere | $A$ |
| Luminous intensity | $I_v$ | candela | $cd$ |
Derived quantities
These are combinations of the fundamental quantities. The following are examples of derived quantities. Note the fundamental quantities which are involved in each. $$ \begin{equation}\begin{aligned} area=length\times width\\ \end{aligned}\end{equation} $$ Width is a length measurement and is essentially Length disguised under another word. This would mean that height, breadth, distance, displacement, perimeter and circumference are also length measurements (they fall under the fundamental quantity Length). $$ \begin{equation}\begin{aligned} volume&=length\times width\times height\\ OR&\\ volume&=area\times height\\ \end{aligned}\end{equation} $$ Notice that area is a derived quantity. Thus volume can be seen as the product of three fundamental quantities (length, width and height) or as the product of a derived quantity (area) and a fundamental quantity (height).
Let’s look at some other examples. $$ \begin{equation}\begin{aligned} speed&=\frac{distance}{time}\\ velocity&=\frac{displacement}{time}\\ acceleration&=\frac{velocity}{time}\\ force&=mass\times acceleration\\ pressure&=\frac{force}{area}\\ \end{aligned}\end{equation} $$
Finding the units of derived quantities
We can find the units of derived quantities if we substitute the units of the other quantities which make it up: $$ \begin{equation}\begin{aligned} speed=\frac{distance}{time}\rightarrow \frac{m}{s}\ OR\ ms^{-1}\\ \end{aligned}\end{equation} $$
Mission details
Find the units of the previously listed derived quantities by making use of their formulae.