Ejercicio resuelto de Física y Química 4 ESO

Usa factores de conversión y efectúa los siguientes cambios de unidades de velocidad:

a) $90\text{ m/s}\to \text{km/h}$
b) $540\text{ km/h}\to \text{m/s}$
c) $\mathrm{4,2}\text{ km/min}\to \text{m/h}$
d) $108\text{ km/h}\to \text{m/s}$
e) $200\text{ cm/s}\to \text{m/min}$
f) $2540\text{ mm/s}\to \text{dm/min}$
g) $4\text{ km/s}\to \text{m/h}$
h) $\mathrm{17,2}\text{ hm/min}\to \text{km/h}$
i) $240\text{ cm/min}\to \text{m/s}$
j) $658\text{ mm/s}\to \text{m/min}$
k) $30\text{ m/s}\to \text{cm/min}$
l) $90\text{ km/h}\to \text{m/min}$

$\mathbf{\text{a)}}$ Un factor para pasar de m a km y otro de s a h:
$90{\displaystyle \frac{\cancel{\text{m}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{1\text{ km}}{1000\cancel{\text{m}}}}\cdot {\displaystyle \frac{3600\cancel{\text{s}}}{1\text{ h}}}={\displaystyle \frac{90\cdot 3600}{1000}}{\displaystyle \frac{\text{km}}{\text{h}}}=324{\displaystyle \frac{\text{km}}{\text{h}}}$


$\mathbf{\text{b)}}$ Un factor para pasar de km a m y otro de h a s:
$540{\displaystyle \frac{\cancel{\text{km}}}{\cancel{\text{h}}}}\cdot {\displaystyle \frac{1000\text{ m}}{1\cancel{\text{km}}}}\cdot {\displaystyle \frac{1\cancel{\text{h}}}{3600\text{ s}}}={\displaystyle \frac{540\cdot 1000}{3600}}{\displaystyle \frac{\text{m}}{\text{s}}}=150{\displaystyle \frac{\text{m}}{\text{s}}}$


$\mathbf{\text{c)}}$ Un factor para pasar de km a m y otro de min a h:
$\mathrm{4,2}{\displaystyle \frac{\cancel{\text{km}}}{\cancel{\text{min}}}}\cdot {\displaystyle \frac{1000\text{ m}}{1\cancel{\text{km}}}}\cdot {\displaystyle \frac{60\cancel{\text{min}}}{1\text{ h}}}=\mathrm{4,2}\cdot 1000\cdot 60{\displaystyle \frac{\text{m}}{\text{h}}}=252000{\displaystyle \frac{\text{m}}{\text{h}}}=\mathrm{2,52}\cdot {10}^5{\displaystyle \frac{\text{m}}{\text{h}}}$


$\mathbf{\text{d)}}$ Un factor para pasar de km a m y otro de h a s:
$108{\displaystyle \frac{\cancel{\text{km}}}{\cancel{\text{h}}}}\cdot {\displaystyle \frac{1000\text{ m}}{1\cancel{\text{km}}}}\cdot {\displaystyle \frac{1\cancel{\text{h}}}{3600\text{ s}}}={\displaystyle \frac{108\cdot 1000}{3600}}{\displaystyle \frac{\text{m}}{\text{s}}}=30{\displaystyle \frac{\text{m}}{\text{s}}}$


$\mathbf{\text{e)}}$ Un factor para pasar de cm a m y otro de s a min:
$200{\displaystyle \frac{\cancel{\text{cm}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{1\text{ m}}{100\cancel{\text{cm}}}}\cdot {\displaystyle \frac{60\cancel{\text{s}}}{1\text{ min}}}={\displaystyle \frac{200\cdot 60}{100}}{\displaystyle \frac{\text{m}}{\text{min}}}=120{\displaystyle \frac{\text{m}}{\text{min}}}$


$\mathbf{\text{f)}}$ Un factor para pasar de mm a dm y otro de s a min:
$2540{\displaystyle \frac{\cancel{\text{mm}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{1\text{ dm}}{100\cancel{\text{mm}}}}\cdot {\displaystyle \frac{60\cancel{\text{s}}}{1\text{ min}}}={\displaystyle \frac{2540\cdot 60}{100}}{\displaystyle \frac{\text{dm}}{\text{min}}}=1524{\displaystyle \frac{\text{dm}}{\text{min}}}$


$\mathbf{\text{g)}}$ Un factor para pasar de km a m y otro de s a h:
$4{\displaystyle \frac{\cancel{\text{km}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{1000\text{ m}}{1\cancel{\text{km}}}}\cdot {\displaystyle \frac{3600\cancel{\text{s}}}{1\text{ h}}}=4\cdot 1000\cdot 3600{\displaystyle \frac{\text{m}}{\text{h}}}=14400000{\displaystyle \frac{\text{m}}{\text{h}}}=\mathrm{1,44}\cdot {10}^7{\displaystyle \frac{\text{m}}{\text{h}}}$


$\mathbf{\text{h)}}$ Un factor para pasar de hm a km y otro de min a h:
$\mathrm{17,2}{\displaystyle \frac{\cancel{\text{hm}}}{\cancel{\text{min}}}}\cdot {\displaystyle \frac{1\text{ km}}{10\cancel{\text{hm}}}}\cdot {\displaystyle \frac{60\cancel{\text{min}}}{1\text{ h}}}={\displaystyle \frac{\mathrm{17,2}\cdot 60}{10}}{\displaystyle \frac{\text{km}}{\text{h}}}=\mathrm{103,2}{\displaystyle \frac{\text{km}}{\text{h}}}$


$\mathbf{\text{i)}}$ Un factor para pasar de cm a m y otro de min a s:
$240{\displaystyle \frac{\cancel{\text{cm}}}{\cancel{\text{min}}}}\cdot {\displaystyle \frac{1\text{ m}}{100\cancel{\text{cm}}}}\cdot {\displaystyle \frac{1\cancel{\text{min}}}{60\text{ s}}}={\displaystyle \frac{240}{100\cdot 60}}{\displaystyle \frac{\text{m}}{\text{s}}}=\mathrm{0,04}{\displaystyle \frac{\text{m}}{\text{s}}}$


$\mathbf{\text{j)}}$ Un factor para pasar de mm a m y otro de s a min:
$658{\displaystyle \frac{\cancel{\text{mm}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{1\text{ m}}{1000\cancel{\text{mm}}}}\cdot {\displaystyle \frac{60\cancel{\text{s}}}{1\text{ min}}}={\displaystyle \frac{658\cdot 60}{1000}}{\displaystyle \frac{\text{m}}{\text{min}}}=\mathrm{39,48}{\displaystyle \frac{\text{m}}{\text{min}}}$


$\mathbf{\text{k)}}$ Un factor para pasar de m a cm y otro de s a min:
$30{\displaystyle \frac{\cancel{\text{m}}}{\cancel{\text{s}}}}\cdot {\displaystyle \frac{100\text{ cm}}{1\cancel{\text{m}}}}\cdot {\displaystyle \frac{60\cancel{\text{s}}}{1\text{ min}}}=30\cdot 100\cdot 60{\displaystyle \frac{\text{cm}}{\text{min}}}=180000{\displaystyle \frac{\text{cm}}{\text{min}}}=\mathrm{1,8}\cdot {10}^5{\displaystyle \frac{\text{cm}}{\text{min}}}$


$\mathbf{\text{l)}}$ Un factor para pasar de km a m y otro de h a min:
$90{\displaystyle \frac{\cancel{\text{km}}}{\cancel{\text{h}}}}\cdot {\displaystyle \frac{1000\text{ m}}{1\cancel{\text{km}}}}\cdot {\displaystyle \frac{1\cancel{\text{h}}}{60\text{ min}}}={\displaystyle \frac{90\cdot 1000}{60}}{\displaystyle \frac{\text{m}}{\text{min}}}=1500{\displaystyle \frac{\text{m}}{\text{min}}}$