Certainly! To convert a speed given in kilometers per hour (km/h) to meters per second (m/s), follow these steps:
1. Understand the relationship between the units:
- 1 kilometer (km) = 1000 meters (m)
- 1 hour (h) = 3600 seconds (s)
2. Set up the conversion factor:
- Since 1 km/h = (1000 meters) / (3600 seconds)
3. Perform the unit conversion:
- To convert from km/h to m/s, multiply the speed in km/h by the conversion factor [tex]\(\frac{1000\ \text{meters}}{3600\ \text{seconds}}\)[/tex].
4. Simplify the conversion factor:
- [tex]\(\frac{1000}{3600} = \frac{10}{36} = \frac{5}{18}\)[/tex]
So, to convert a speed [tex]\( x \)[/tex] kilometers per hour into meters per second, use the following relation:
[tex]\[ \text{Speed in m/s} = x \times \frac{5}{18} \][/tex]
### Example Conversion
Let's say we have [tex]\( x = 54 \)[/tex] km/h.
1. Multiply [tex]\( 54 \)[/tex] km/h by [tex]\(\frac{5}{18}\)[/tex]:
[tex]\[ \text{Speed in m/s} = 54 \times \frac{5}{18} \][/tex]
2. Perform the multiplication:
[tex]\[ 54 \times \frac{5}{18} = 3 \times 5 = 15 \][/tex]
So, [tex]\( 54 \)[/tex] km/h is equivalent to [tex]\( 15 \)[/tex] m/s.
### General Formula
For any speed [tex]\( x \)[/tex] km/h, the conversion to m/s can be simplified to:
[tex]\[ \text{Speed in m/s} = x \times \frac{5}{18} \][/tex]
This formula can be used to convert any speed from kilometers per hour to meters per second.
