Calculating Train Speed in km/h
The problem asks us to find the speed of a train in kilometers per hour (km/h), given the distance it travels in meters (m) and the time taken in seconds (s).
Step 1: Calculate Speed in m/s
First, calculate the speed in meters per second (m/s) using the formula:
Speed = \(\frac{Distance}{Time}\)
Given:
- Distance = 45 m
- Time = 3 s
Calculation:
Speed = \(\frac{45 \text{ m}}{3 \text{ s}}\) = 15 m/s
Step 2: Convert Speed from m/s to km/h
To convert speed from meters per second (m/s) to kilometers per hour (km/h), we use the conversion factor \(\frac{18}{5}\). This factor comes from:
- 1 km = 1000 m
- 1 h = 3600 s
- Therefore, 1 m/s = \(\frac{1 \text{ m}}{1 \text{ s}} = \frac{1/1000 \text{ km}}{1/3600 \text{ h}} = \frac{3600}{1000} \text{ km/h} = \frac{18}{5} \text{ km/h}\)
Now, convert the calculated speed:
Speed (km/h) = Speed (m/s) \(\times\) \(\frac{18}{5}\)
Speed (km/h) = 15 \(\times\) \(\frac{18}{5}\)
Speed (km/h) = 3 \(\times\) 18
Speed (km/h) = 54 km/h
Conclusion
The speed of the train is 54 km/h. This corresponds to Option D.
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