Question

A man covers $36km$ in $1hr$. Find his speed in $m{{s}^{-1}}$.

Answer 1

Hint: Thousand metres is equal to one kilometre. One hour is equal to sixty minutes. One minute is equal to sixty seconds. Speed is equal to the ratio of distance and time. To change $km{{(hr)}^{-1}}$ to $m{{s}^{-1}}$, we have to do necessary conversions.
Formula used:
$s=\dfrac{d}{t}$

Complete answer:
We are told that a man covers a distance of $36km$. The time required for him to cover this distance is equal to $1hr$. We are required to calculate the speed of this person in $m{{s}^{-1}}$.
We know that speed is defined as the ratio of distance covered to the time taken to cover this distance. Mathematically, speed is given by
$s=\dfrac{d}{t}$
where
$s$ is the speed of a person or an object
$d$ is the distance covered by the person or the object
$t$ is the time required by the person or the object to cover the distance
Let this be equation 1.
Since we are provided that the distance covered by the person is $36km$ and time taken by the person to cover this distance is equal to $1hr$, speed of the person can be easily determined using equation 1.
Calculating the speed using equation 1, we have
$s=\dfrac{d}{t}=\dfrac{36km}{1hr}=36km{{(hr)}^{-1}}$
where
$s$ is the speed of the person
$d=36km$, is the distance covered by the person
$t=1hr$, is the time taken by the person to cover $36km$
Clearly, the speed of the person is $36km{{(hr)}^{-1}}$.
But we are asked to calculate the speed of the person in $m{{s}^{-1}}$. So, this answer is not enough. We have to convert our calculated speed into $m{{s}^{-1}}$. For this, let us go through some conversions as given below.
We know that a thousand metres is equal to one kilometre. Also do we know that one hour is equal to sixty minutes and one minute is equal to sixty seconds. Writing down these statements mathematically, we have
$\begin{align}
  & 1km=1000m \\
 & 1hr=60\min \\
 & 1\min =60s \\
\end{align}$
Combining the last two expressions given above, we have
$1hr=60\min \times 60s=3600s$
Now, let us use these conversion formulas to convert the calculated speed of the person in $km{{(hr)}^{-1}}$ to $m{{s}^{-1}}$.
Clearly, we have
$36km{{(hr)}^{-1}}=36\times 1000m{{(3600s)}^{-1}}=\dfrac{36000}{3600}m{{s}^{-1}}=10m{{s}^{-1}}$

 Therefore, the speed of the person in $m{{s}^{-1}}$ is equal to $10m{{s}^{-1}}$.

 Note:
Students need to be aware of conversion formulas as given in the solution above. They should also have a basic idea of when to express speeds in $km{{(hr)}^{-1}}$ as well as $m{{s}^{-1}}$. Usually, high speeds like those of vehicles are expressed in $km{{(hr)}^{-1}}$ whereas speeds like those of humans and animals are expressed in $m{{s}^{-1}}$.