Question

Which speed is greater: $30$m/s or $30$km/h?

Answer 1

Hint: First, in the given question we have to convert the given terms into common expressions so that only we are able to say which one is greater speed.
So, we will convert the given terms as a meter per second into the kilometer per hour and compare both values to find which one is greater.
First, convert the hours into minutes and then convert the minutes into the seconds so that there is no confusion in the division terms for hours to seconds.

Formula used: We are using the formula of kilometer to meter and hours to seconds, that is $1km = 1000m$and $1h = 3600s(60m \times 60s)$

Complete step by step answer:
From that, we have $30$m/s and $30$km/h.
To compare the two values, convert them as one unit represented in meters and seconds.
So don’t convert the second expression $30$km/h
Take the first expression $30$m/s and convert them into meters per second using the formula above.
Thus, we get, $1km = 1000m \Rightarrow 1m = \dfrac{1}{{1000}}km$and $1h = 3600s(60m \times 60s) \Rightarrow 1s = \dfrac{1}{{3600}}h$
This implies that, $1\dfrac{m}{s} = \dfrac{1}{{1000}}km \times 3600h$
Thus, solving this we get, $1\dfrac{m}{s} = \dfrac{1}{{1000}}km \times 3600h \Rightarrow 3.6$km/h
Now multiple both values into $30$, then we get $30$m/s = $30(3.6)$km/h
Thus, by the multiplication operation, we get $30$m/s = $30(3.6)$km/h $\Rightarrow 108$km/h
Therefore, we converted the first value $30$ m/s as $108$km/h
Hence compare the two values we get, \[108\]km/h > \[30\]km/h
Therefore, we get \[108\] km/h > \[30\]km/h and $108$km/h is the greatest speed. That means $30$m/s is the greatest speed.

Note: To convert the meters into kilometers by dividing, then convert second to the hour by again dividing, and then we combine them both to get the required relation.
Important that we know that formula and where to use them.
We can also able to convert the $30$km/h to meter per seconds and find the value, to check which one is greater, we get the same result as $30$m/s is the greatest speed
The general expression for kilometer per hour to meter per seconds is $1$km/h= $\dfrac{5}{{18}}$m/s