# [Physics] the name and symbol of the derived unit for one thousand metres?

metrologysi-unitsunits

I'm still getting confused of what a derived unit is. I used the internet to find an answer but I'm still getting confused.

• $\mathrm{km}$, $\mathrm{miles}$ and $\mathrm{hr}$ are units (one of them with a prefix).
• $\mathrm{miles/hr}$ and $\mathrm L$ (litre) are derived units.

In the SI system:

• $\mathrm m$ and $\mathrm s$ are SI base units.
• $\mathrm{km}$ and $\mathrm{ms}$ are SI units with prefixes (not called base but also not derived).
• $\mathrm{m/s}$, $\mathrm{m^3}$ and $\mathrm{km^3}$ are derived SI units (one with a prefix).

You must start somewhere, when deriving something. That is why we start out by defining some more or less randomly chosen set of base units. The SI system has defined seven base SI units: $$\mathrm{s, m, K, A, cd, kg, mol}\\ \mathrm{(second, metre, Kelvin, Ampere, candera, kilogram, mole)}$$

The SI system has tried to define enough base units to cover everything. In other words, they try to define enough base quantities (time, length, mass, etc.) to describe everything in the Universe. And each base quantity is given a base SI unit. Every other quantity are derived from those base quantities (veloticy is lenth per time etc.). And their units are thus derived from the base units ($\mathrm{m/s}$ is $\mathrm m$ per $\mathrm s$).

Note that adding prefixes doesn't make a unit derived. It is just some multiples of the unit.

Also note that some derived units have gotten specific names, such as

$$\mathrm{N, Hz, J, C, V, \Omega, W,\cdots}\\ \mathrm{(Newton, Herz, Joule, Coulomb, Volt, Ohm, Watt,\cdots)}$$

The wikipedia article gives a good overview.

I deliberately say base quantities rather than fundamental quantities because the SI unit's purpose is not to choose the most fundamental set but just a complete set. Otherwise an Amp, a kilogram and a mole would never have been included in their forms.

What is the name and symbol of the derived unit for one thousand metres?

From the explanation above, there is no answer to this question of yours. One thousand metres is not a derived quantity. It is still a length quantity. So it has the unit of metres: $1000\;\mathrm m$, but can be shortened with a prefix to for example kilometres: $1\;\mathrm{km}$ (or megametres: $0.001\;\mathrm{Mm}$ or millimetres: $1000000\;\mathrm{mm}$ and so on). Not a derived unit, just a mutiple of the metre unit.