1.2.2 Derived Quantities

Derived Quantities

A derived quantity is a Physics quantity that is not a base quantity. It is the quantities which derived from the base quantities through multiplying and/or dividing them.Example

(Speed is derived from dividing distance by time.)

Derived Unit
The derived unit is a combination of base units through multiplying and/or dividing them.
Example 1
Find the derived unit of density.
Answer
Unit Conversion
Area and Volume
Example 2
Convert the unit of length, area and volume below to the units given.
a) 7.2 m = ____________cm
b) 0.32 m² = ____________cm²c) 0.0012 m³ = ____________cm³d) 5.6 cm = ____________m
e) 350 cm² = ____________m²f) 45000 cm³ = ____________m³Answer
a) 7.2 m = 7.2 x 10² cm
b) 0.32 m² = 0.32 x 10⁴ cm² = 3.2 x 10³ cm²
c) 0.0012 m³ = 0.0012 x 10⁶ cm³ = 1.2 x 10³ cm³
d) 5.6 cm = 5.6 x 10^-2 m
e) 350 cm² = 350 x 10^-4 m² = 3.5 x 10^-2 m²
f) 45000 cm³ = 45000 x 10^-6 m³ = 4.5 x 10^-2 m³

Speed
Example 3
Complete the following unit conversion
a) 12 kmh^-1 = __________ ms^-1
b) 12 ms^-1 = __________ kmh^-1

Answer


a) \[\begin{array}{l} 12km{h^{ - 1}}\\ = \frac{{12km}}{{1h}}\\ = \frac{{12000m}}{{60 \times 60s}}\\ = 3.33m{s^{ - 1}} \end{array}\]

b)
\[\begin{array}{l} 12m{s^{ - 1}}\\ = \frac{{12m}}{{1s}}\\ = \frac{{\frac{{12}}{{1000}}km}}{{\frac{1}{{3600}}h}}\\ = 43.2km{h^{ - 1}} \end{array}\]