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 = ____________cm²
c) 0.0012 m³ = ____________cm³
d) 5.6 cm = ____________m
e) 350 cm² = ____________m²
f) 45000 cm³ = ____________m³
Answer
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){\rm{  12kmh}}^{{\rm{ - 1}}} {\rm{ = }}{{{\rm{12km}}} \over {{\rm{1h}}}}{\rm{ = }}{{{\rm{12,000m}}} \over {{\rm{60 \times 60s}}}}{\rm{ = }}{{{\rm{10}}} \over {\rm{3}}}{\rm{ms}}^{{\rm{ - 1}}}

b){\rm{  12ms}}^{{\rm{ - 1}}} {\rm{ =  }}{{{\rm{12m}}} \over {{\rm{1s}}}}{\rm{ = }}{{{{{\rm{12}}} \over {{\rm{1000}}}}{\rm{km}}} \over {{{\rm{1}} \over {{\rm{60 \times 60}}}}{\rm{h}}}}{\rm{ = 43}}{\rm{.2kmh}}^{{\rm{ - 1}}}

External Link
International System of Unit


Interactive Animation