Question

In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably more comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical intuition. More precisely, show that (a) 1.0m/s=3.6km/h and (b) 1.0m/s=2.2mi/h.

(a) (1.0) m/s = (3.6) km/h
a) (1.0) m/s = (3.6) km/h
b) (1.0) m/s = (2.2) mi/h
c) (1.0) m/s = (4.0) km/h
d) (1.0) m/s = (1.0) km/h

(b) (1.0) m/s = (2.2) mi/h
a) (1.0) m/s = (3.6) km/h
b) (1.0) m/s = (2.2) mi/h
c) (1.0) m/s = (4.0) km/h
d) (1.0) m/s = (1.0) km/h

Answer 1

To convert 1.0 m/s to km/h, you multiply by the ratio of 3600 seconds per hour and invert the ratio of 1000 meters per kilometer to get 3.6 km/h. Similarly, to convert to mi/h, use the conversion that 1 mile is 1609.34 meters, which results in approximately b) (1.0) m/s = (2.2) mi/h.

Step-by-step explanation:

Converting speeds between different units of measurement is an important skill in physics and is often used to ensure that calculations are done in the correct units for a given context. To convert the speed from meters per second (m/s) to kilometers per hour (km/h), you can use the conversion factor where 1 km equals 1000 meters, and 1 hour equals 3600 seconds. Therefore:

To show that 1.0 m/s = 3.6 km/h:

1.0 m/s × (1 km/1000 m) × (3600 s/1 h) = 3.6 km/h.

To show that 1.0 m/s = 2.2 mi/h:

1.0 m/s × (1 mi/1609.34 m) × (3600 s/1 h) = 2.23694 mi/h, which is approximately 2.2 mi/h.

The correct options are therefore:

(a) 1.0 m/s = 3.6 km/h

(b) 1.0 m/s = 2.2 mi/h

It is always good to check if the answer seems reasonable by considering known information, such as how far one would travel in a given amount of time at a certain speed. These conversions are not only useful in academic settings but also in everyday situations, like understanding speed limits when driving in different countries.