Determine the conversion factor between (a) km/h and mi/h, (b) m/s and ft/s, and (c) km/h and m/s.

Whenever a quantity is measured, the numerical value of the quantity is written along with its unit. To convert one set of units of a quantity into another, the quantity is multiplied or divided by a certain number known as the conversion factor.

For example, if the length of a wooden box is 6.00 inches and you want to measure it in centimeters, you can do this by multiplying the length of the box by its conversion factor. The conversion factor to convert inches into centimeters is \(1\;{\rm{in}} = 2.54\;{\rm{cm}}\)

Thus, the length of the wooden box in centimeters will be

\(\begin{aligned}{l}6.00\;{\rm{in}} = \left( {6.00\;{\rm{in}}} \right) \times \left( {2.54\;\frac{{{\rm{cm}}}}{{{\rm{in}}}}} \right)\\ \Rightarrow 6.00\;{\rm{in}} = 15.2\;{\rm{cm}}{\rm{.}}\end{aligned}\)

Here, km/h and mi/h are the units of speed. You know that speed is defined as the distance traveled per unit time. Here, time in both units is given in hours. Thus, you need to convert only the units of distance; i.e., km into miles.

Start performing this conversion by using the conversion factor \(1\,\,{\rm{km}} = 1000\,\,{\rm{m}}\). Also, you know that Step 3: Conversion factor between m/s and ft/s Using these conversion factors, you can write 1 km as follows:

\(\begin{aligned}{c}1\,\,{\rm{km}} = \left( {1000\,\,{\rm{m}}} \right) \times \left( {100\frac{{{\rm{cm}}}}{{\rm{m}}}} \right) \times \left( {\frac{{1\,\,{\rm{in}}}}{{2.54\,\,{\rm{cm}}}}} \right) \times \left( {\frac{{1\,\,{\rm{ft}}}}{{12\,\,{\rm{in}}}}} \right) \times \left( {\frac{{1\,\,{\rm{mi}}}}{{5280\,\,{\rm{ft}}}}} \right)\\ = 0.62\,\,{\rm{mi }}\end{aligned}\)

The result has been rounded off to two decimal places.

Thus, 1 km/h can be written as 1 km/h = 0.62 mi/h.

Hence, the conversion factor between km/h and mi/h is 1 km/h = 0.62 mi/h.

Here, m/s and ft/s are also the units of speed. Moreover, time in both the units is given in seconds. Thus, you need to convert only the units of distance; i.e., m into ft.

Start performing this conversion by using the conversion factor \(1\,\,{\rm{m}} = 100\,\,{\rm{cm}}\). You also know that there are 2.54 cm in an inch and 12 inches in a foot. Using these conversion factors, you can write 1 m as follows:

\(\begin{aligned}{c}1\,\,{\rm{m}} = \left( {100\,\,{\rm{cm}}} \right) \times \left( {\frac{{1\,\,{\rm{in}}}}{{2.54\,\,{\rm{cm}}}}} \right) \times \left( {\frac{{1\,\,{\rm{ft}}}}{{12\,\,{\rm{in}}}}} \right)\\ = 3.28\,\,{\rm{ft}}\end{aligned}\)

The result has been rounded off to two decimal places.

Thus, 1 m/s can be written as 1 m/s = 3.28 ft/s.

Hence, the conversion factor between m/s and ft/s is 1 m/s = 3.28 ft/s.

Here, both km/h and m/s are the units of speed. You know that speed is defined as the distance traveled per unit time. You need to convert the units of distance, i.e., kilometer into meter, and the units of time; i.e., an hour into second.

You know that there are 1000 m in a kilometer and 3600 s in an hour. Using these conversion factors, 1 km/h can be written as follows:

\(\begin{aligned}{c}1\,\,\frac{{{\rm{km}}}}{{\rm{h}}} = \left( {1000\,\,\frac{{\rm{m}}}{{\rm{h}}}} \right) \times \left( {\frac{{{\rm{1 h}}}}{{{\rm{3600 s}}}}} \right)\\ = 0.28\,\,\frac{{\rm{m}}}{{\rm{s}}}.\end{aligned}\)

The result has been rounded off up to two decimal places.

Thus, the conversion factor between km/h and mi/h is 1 km/h = 0.28 m/s.