The formula to convert meters per second [m/s] to kilometres per hour [km/h] is given by:

$$v_{(km/h)} = 3.6 \times v_{ (m/s) }$$

Where:

• $v_{ (m/s) }$ is the linear speed expressed in meters per second
• $v_{ (km/h) }$ is the linear velocity expressed in kilometres per hour.

Here is an online converter from m/s to km/h

To convert meters per second (m/s) to kilometers per hour (km/h), you use the following formula:

$$\text{Speed in km/h} = \text{Speed in m/s} \times 3.6$$

Explanation:

The relationship between meters per second (m/s) and kilometers per hour (km/h) is based on unit conversion:

• 1 kilometer (km) equals 1,000 meters (m).
• 1 hour equals 3,600 seconds.

Let's detail the conversion step by step :

1. Let's convert meters per second (m/s) to kilometers per second (km/s).

$$v_{(km/s)} = \frac{ v_{(m/s)}}{1000}$$

2. Let's now convert kilometers per second (km/s) to kilometers per hour (km/h).

$$v_{(km/h)} = 3600 \times v_{(km/s)}$$

3. By merging both conversion, we get:

$$v_{(km/h)} = \frac{3600}{1000} \times v_{(m/s)}$$

$$v_{(km/h)} = 3.6 \times v_{(m/s)}$$

So, the formula is:

$$\text{Speed in km/h} = \text{Speed in m/s} \times 3.6$$

Example:

Let's say you have a speed of 10 meters per second (m/s), and you want to convert it to kilometers per hour (km/h).

1. Given speed: $10 \, \text{m/s}$
2. Use the formula:

$$\text{Speed in km/h} = \text{Speed in m/s} \times 3.6$$

3. Substitute the value:

$$\text{Speed in km/h} = 10 \, \text{m/s} \times 3.6 = 36 \, \text{km/h}$$

Conclusion: a speed of 10 m/s is equal to 36 km/h.