Question

Equivalent speed to $25{\text{m}}/{\text{sec}}\;$ is:
A. $75{\text{km}}/{\text{hr}}\;$
B. $80{\text{km}}/{\text{hr}}\;$
C. $90{\text{km}}/{\text{hr}}\;$
D. $100{\text{km}}/{\text{hr}}\;$

Answer 1

Hint: From the above question and based on options, it is clear that we need to convert metre per second into kilometre per hour. So, we need to know the conversions of length and conversions of time. So, we need to convert kilometers per hour from meters per second.

Complete step by step answer:
So, according to the question, it is given as $25{\text{m}}/{\text{sec}}\;$.
Definition of speed: Measured at distance travelled per unit of time.
Definition of metre: A metre is a decimal multiple of the centimetre, the standard unit of length, approximately equivalent to 39.37 inches.
A kilometre is now what we use officially for expressing the distance between two places or points.
Definition of kilometre: A kilometre is a decimal multiple of metre, the standard international unit of length.
Therefore,
$\begin{align}
  & 1\text{ km}=1000\text{ metre} \\
 & \Rightarrow 1\text{ metre}=\dfrac{1\text{ km}}{1000} \\
\end{align}$
Definition of hour: A period of time equal to 60 minutes that is 3600 seconds.
Definition of second: It is measured as the smallest unit of time, $\Rightarrow 1\text{ sec}=\dfrac{1}{3600}\text{ hr}$.
Now we have to convert $25{\text{m}}/{\text{sec}}\;$ in ${\text{km}}/{\text{hr}}\;$. So,
$\begin{align}
  & x=25{\text{m}}/{\text{sec}}\; \\
 & \Rightarrow x=25\times \left( \dfrac{1}{1000} \right).\left( 3600\text{ }{\text{s}}/{\text{h}}\; \right) \\
 & \Rightarrow x=25\left( \dfrac{3600\times 1}{1000\times 1} \right) \\
 & \Rightarrow x=25\left( 3.6 \right) \\
 & \Rightarrow x=90\text{ }{\text{km}}/{\text{hr}}\; \\
\end{align}$

So, the correct answer is “Option C”.

Note: If the problem is to convert kilometre to metre, then there is a standard equation for this type of conversion. To convert a kilometre per hour into metre per second, we need to multiply by 5 and divide it by 18. This standard form for this is given as: $\dfrac{{1km}/{1000}\;}{1{hr}/{3600}\;}$.