Calculating Train Speed in km/h
The question asks for the speed of a train in kilometers per hour (km/h). We are given the train's length and the time it takes to cross a stationary man.
Key Information Provided
- Train Length: 120 meters
- Time to Cross Man: 6 seconds
Speed Calculation Steps
To find the speed of the train, we use the formula: Speed = Distance / Time.
- Determine the Distance: When a train crosses a man (or a pole), the distance the train covers is equal to its own length.
Distance = 120 meters
- Calculate Speed in m/s: Use the given time to find the speed in meters per second.
Speed (m/s) = \(\frac{\text{Distance}}{\text{Time}}\) = \(\frac{120 \text{ m}}{6 \text{ s}}\) = 20 m/s
- Convert Speed to km/h: To convert meters per second (m/s) to kilometers per hour (km/h), multiply by the conversion factor \(\frac{18}{5}\).
Speed (km/h) = Speed (m/s) \(\times\) \(\frac{18}{5}\)
Speed (km/h) = 20 \(\times\) \(\frac{18}{5}\)
Speed (km/h) = 4 \(\times\) 18
Speed (km/h) = 72 km/h
The speed of the train is 72 km/h.
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