Question

How do you convert $km/h{\text{ to }}m/s{\text{?}}$

Answer 1

Hint: The given question is based on distance and time. Where $km$ and $m$ are the units of distance and $h$ and $s$ are the units of time. There are different identities to convert one distance unit to another. The given question is about the conversion of units. We apply the identity of distance.
Units then cancelled out the terms. Again, we apply the identity of time units then cancel out the terms. In that way, we can find the solution of a given problem.

Complete step-by-step answer:
We have to convert $km/h$ to $m/s$ .
$km$ is the units of distance $m$ is the unit of distance. As $km$ is $kilometre$ and $m$ is meter.
As $h$ is the hour which usually represents the time.
and $s$ is second, which is also included as time.
As $km/h$ , it represents $km$ per hour and we can say that how much distance is covered in per hour.
As represents the meter per second or we can say that how much distance in metres covered per second.
Let considered be the number which represents distance covered $km/h$ so, it becomes.
$\dfrac{{xkm}}{h}{\text{ }}.....................{\text{(A)}}$
We have to convert $km$ to $m$ . So, let us take identity of
$1km = 1000m$
So, we have to multiply the equation (A) with $\dfrac{{1000m}}{{1km}}$
we get-
$\dfrac{{xkm}}{h}{\text{ }} \times \dfrac{{1000m}}{{1km}}$
Cancel the $m$ units we get
$ \Rightarrow \dfrac{{xkm}}{h}{\text{ }} \times \dfrac{{1000m}}{{1km}}{\text{ }}..................{\text{(B)}}$
Let us take identity of $1hour = 3600\sec $ or we can say that there are $3600\sec $ in $1$ hour
Multiply the equation (B) with $\dfrac{{1h}}{{3600\sec }}$
we get \[\dfrac{x}{h} \times \dfrac{{1000m}}{1} \times \dfrac{{1h}}{{3600\sec }}\]
Cancelled the units of hours ( $h$ ) and we are left with units of $m/s$. So the equation
\[\dfrac{x}{h} \times \dfrac{{1000m}}{1} \times \dfrac{{1h}}{{3600\sec }}\]
\[ \Rightarrow \dfrac{{x{\text{ }}1000m}}{{3600\sec }}\]
By simplifying \[\dfrac{{1000}}{{3600}}\] we get \[\dfrac{{10}}{{36}}\]
So,
$ = \dfrac{{10x}}{{36}}m/s$
where $m/s$ is meter per second. Simplify \[\dfrac{{10}}{{36}}\] we get \[\dfrac{5}{{18}}\] so,
the equation becomes $\dfrac{{5x}}{{18}}m/s$
In that way we can convert the $km/h$ to $m/s$.

Note: The given question is based on the distance and time. It is basically about the conversion of distance and time from one unit to another. The distance can be measured in different units like meter, kilometer, centimeter so on…. The identities to measure these units and to convert them the identities of distance and time and conclude our result.