Question

Express $36km{h^{ - 1}}$ in $m{s^{ - 1}}$ .
Express $15m{s^{ - 1}}$ in $km{h^{ - 1}}$ .

Answer 1

Hint : To convert the first one we just convert the kilometers into meters and the hour to seconds by simply doing it in fractions.
For the second one there are sixty minutes with sixty seconds in an hour. That would give us $3600$ seconds. So $15m{s^{ - 1}}$ would be $54000$ meters. Dividing it by $1000$ we get the answer.

Complete Step By Step Answer:
In order to convert $36km{h^{ - 1}}$ into $m{s^{ - 1}}$ we first write $36km{h^{ - 1}}$ into fraction,
So, it can be written as $\dfrac{{36km}}{h}$ .
Since a kilometer contains one thousand meters and an hour contains sixty minutes with sixty seconds.
Now;
\Rightarrow \dfrac{{36km}}{h} = \dfrac{{36 \times 1000m}}{{60 \times 60\sec }} \\\ \Rightarrow \dfrac{{36000m}}{{3600\sec }} = \dfrac{{10m}}{{\sec }} \\\ = 10m{s^{ - 1}} \\\
So $10m{s^{ - 1}}$ is the solution.
Now, in order to convert $15m{s^{ - 1}}$ into $km{h^{ - 1}}$ , as there are sixty minutes in an hour where each minute contains sixty seconds.
So an hour would make $3600$ seconds.
$15m{s^{ - 1}}$ For $3600$ seconds would be $54000$ meters.
Now there are thousands of meters in a kilometer. So taking $54000$ and then dividing it by thousand gives us the answer.
\dfrac{{54000}}{{1000}}km{h^{ - 1}} \\\ = 54km{h^{ - 1}} \\\
So $54km{h^{ - 1}}$ is the solution.

Note :
We also directly get the answer by just simply multiplying it by $\dfrac{5}{{18}}$ for the first one.
$\dfrac{5}{{18}}$ Is basically the conversion factor.
$\dfrac{5}{{18}}$ , this basically is used to convert kilometers per hour into meters per seconds.
For the second one, we also get the answer by multiplying it by $36$ thousand and then divide it by a thousand to get the kilometer one. There are sixty minutes in an hour where each minute contains sixty seconds. So an hour would make $3600$ seconds. $15m{s^{ - 1}}$ For $3600$ seconds would be $54000$ meters.