Problem — Elementary conversions

Problem

Convert $1$ hour into seconds and $72\;\text{km/h}$ into metres per second.

Solution

Step 1 — One hour in seconds. We multiply by unit conversion factors so that the unwanted units cancel:

$1\;\text{h} = 1\;\text{h}\cdot \frac{60\;\text{min}}{1\;\text{h}}\cdot \frac{60\;\text{s}}{1\;\text{min}} = 3600\;\text{s} = \ev{3{,}6\cdot 10^3\;\text{s}}$

Step 2 — From km/h to m/s. We convert separately the kilometre into metres ($1\;\text{km} = 10^3\;\text{m}$) and the hour into seconds ($1\;\text{h} = 3600\;\text{s}$):

$72\;\frac{\text{km}}{\text{h}} = 72\cdot \frac{10^3\;\text{m}}{3600\;\text{s}} = \frac{72\,000}{3600}\;\frac{\text{m}}{\text{s}} = \ev{20\;\text{m/s}}$

Remark — the practical rule. The factor $\dfrac{10^3}{3600} = \dfrac{1}{3{,}6}$ shows that one goes from km/h to m/s by dividing by $3{,}6$ (and conversely by multiplying by $3{,}6$): indeed $72 \div 3{,}6 = 20$, consistent with the conversion arrow in the figure.

Linked atoms

Argomenti: Physical quantities and measurement Competenze: Unit conversion Metodi: Conversion factor method