Question

How do I convert $m/s$ to $km/h$? Give an example

Answer 1

Conversion from $m/s$ to $km/h$:

1. Meters per second $\left(m/s\right)$ and kilometers per hour $\left(km/h\right)$ are units of speed (scalar) and velocity (vector).
2. Kilometers per hour $\left(km/h\right)$ measures the distance covered in number of kilometers per one hour and meters per second $\left(m/s\right)$ measures the distance covered in number of meters per one second.
3. To convert meters into kilometers, the quantity is divided by $1000$ and to convert seconds into hours, the quantity is divided by $3600$.
4. So, to convert $m/s$ to $km/h$, the numerator must be divided by $1000$ and the denominator must be divided by $3600$. This implies that the whole quantity that is given in $m/s$ must be multiplied by $\frac{3600}{1000}$.
5. Converting it in least form, the quantity given in $\mathit{m}\mathbf{/}\mathit{s}$ must be multiplied by $\frac{\mathbf{18}}{\mathbf{5}}$ to convert it into $\mathit{k}\mathit{m}\mathbf{/}\mathit{h}$.

Example:

1. Take the speed to be $10m/s$.
2. Multiply this by $\frac{18}{5}$ to convert it into $km/h$.
3. So, $\begin{array}{rcl}10m/s& =& 10\times \frac{18}{5}km/h=36km/h\end{array}$

Hence, the quantity given in $\mathit{m}\mathbf{/}\mathit{s}$ must be multiplied by $\frac{\mathbf{18}}{\mathbf{5}}$ to convert it into $\mathit{k}\mathit{m}\mathbf{/}\mathit{h}$. For example,$\begin{array}{rcl}\mathbf{10}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}& \mathbf{=}& \mathbf{10}\mathbf{\times }\frac{\mathbf{18}}{\mathbf{5}}\mathbf{}\mathit{k}\mathit{m}\mathbf{/}\mathit{h}\mathbf{=}\mathbf{36}\mathbf{}\mathit{k}\mathit{m}\mathbf{/}\mathit{h}\end{array}$.