A train 100 m long passes a platform 100 m long in 10 seconds. The speed of the train is
72 kmph
Determining Train Speed When Passing a Platform
This question asks for the speed of a train given its length, the length of a platform it passes, and the time it takes to complete the passage. We need to calculate the speed in kilometers per hour (kmph).
Key Concepts for Train Problems
When calculating the speed of a train passing a stationary object like a platform, bridge, or tunnel, the total distance covered is the sum of the train's length and the object's length. This is because the train starts passing the object when its front end reaches the beginning of the object, and finishes passing when its rear end leaves the end of the object.
- Train Length: 100 m
- Platform Length: 100 m
- Time Taken: 10 seconds
Calculating Total Distance Covered
To find the speed, we first need the total distance the train travels to completely pass the platform.
The formula is:
\(\text{Total Distance} = \text{Length of Train} + \text{Length of Platform}\)
Substituting the given values:
\(\text{Total Distance} = 100 \, \text{m} + 100 \, \text{m}\)
\(\text{Total Distance} = 200 \, \text{m}\)
Calculating Speed in Meters per Second (m/s)
Speed is defined as distance traveled per unit of time. The basic formula is:
\(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)
Using the calculated total distance and the given time:
\(\text{Speed} = \frac{200 \, \text{m}}{10 \, \text{s}}\)
\(\text{Speed} = 20 \, \text{m/s}\)
Converting Speed to Kilometers Per Hour (kmph)
The question asks for the speed in kmph. To convert from meters per second (m/s) to kilometers per hour (kmph), we use a standard conversion factor.
The conversion factor is:
\(1 \, \text{m/s} = \frac{18}{5} \, \text{kmph}\)
Now, we apply this factor to the speed we calculated:
\(\text{Speed (kmph)} = 20 \, \text{m/s} \times \frac{18}{5} \, \frac{\text{kmph}}{\text{m/s}}\)
Let's perform the calculation:
\(\text{Speed (kmph)} = \frac{20 \times 18}{5}\)
Simplify the expression:
\(\text{Speed (kmph)} = 4 \times 18\)
\(\text{Speed (kmph)} = 72 \, \text{kmph}\)
Conclusion
The calculated speed of the train is 72 kmph.
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