Question

How do I convert \[m/s\] to \[km/h\]?

Answer 1

Hint: In the given question, we have to convert meter per second to kilometer per hour. For that, we convert the meters to kilometers by dividing, then convert second to hour by dividing again, and then we combine them both to get the required relation.

Formula Used:
We are going to use the relation of meter to kilometer and second to hour,
\[1km = 1000m\] and \[1h = 3600s\]

Complete step-by-step answer:
In the given question, we have to convert any given \[m/s\] to \[km/h\].
Let the given speed be \[x{\rm{ }}m/s\].
We know, \[1km = 1000m \Rightarrow 1m = \dfrac{1}{{1000}}km\]
and \[1h = 3600s \Rightarrow 1s = \dfrac{1}{{3600}}h\]
Hence, \[x{\rm{ }}m/s = x \times \dfrac{{\dfrac{1}{{1000}}}}{{\dfrac{1}{{3600}}}} = x \times \dfrac{{36{{00}}}}{{10{{00}}}} = \dfrac{{18}}{5}x{\rm{ }}km/h\]
Thus, to convert meter per second to kilometer per hour, we multiply the given meter per second by \[\dfrac{{18}}{5}\].

Additional Information:
In the given question, we had to convert meter per second to kilometer per hour. But if we had to do the reverse – km/h to m/s, we would have inverted it. For that, we convert the kilometer to meter by multiplying, then convert hour to second by again multiplying, and then we combine them both to get the required relation. Hence,
\[1km/h = \dfrac{5}{{18}}m/s\]

Note: To convert meters to kilometers by dividing, then convert second to hour by again dividing, and then we combine them both to get the required relation. So, it is really important that we know the formulae and where, when and how to use them so that we can get the correct result.