Speed Conversion: km/h to m/s
This solution explains how to convert a given speed from kilometers per hour (km/h) to meters per second (m/s).
Given Speed
The speed of the train is provided as:
$180 \ \text{km/h}$
Conversion Factor Explained
To convert speed from km/h to m/s, we use the relationship between kilometers and meters, and hours and seconds.
- 1 kilometer = 1000 meters
- 1 hour = 3600 seconds
Therefore, the conversion factor is:
$1 \ \text{km/h} = \frac{1000 \ \text{m}}{3600 \ \text{s}} = \frac{5}{18} \ \text{m/s}$
Calculating Speed in m/s
Multiply the speed in km/h by the conversion factor $\frac{5}{18}$:
$ \text{Speed (m/s)} = 180 \ \text{km/h} \times \frac{5}{18} \ \frac{\text{m/s}}{\text{km/h}} $
Perform the calculation:
$ \text{Speed (m/s)} = \frac{180}{18} \times 5 $
$ \text{Speed (m/s)} = 10 \times 5 $
$ \text{Speed (m/s)} = 50 \ \text{m/s} $
Final Result
The train's speed expressed in meters per second is 50 m/s.
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