Step 1: Understanding the Concept:
When solving problems involving trains crossing objects, the definition of "distance" depends entirely on the nature of the object being crossed.
In this scenario, the train is crossing a platform, which is a stationary object with a significant length of its own.
To "completely cross" the platform, the front of the train must first enter the platform, travel the entire length of the platform, and then the entire length of the train must also exit the platform.
Therefore, the total distance covered by the engine from the moment it enters until the last carriage leaves is the sum of the train's length and the platform's length.
This is a fundamental concept in relative motion where one object has a fixed dimension.
Additionally, the units provided in the question are meters and seconds, but the options are in kilometers per hour.
This requires a two-stage process: first calculating the speed in meters per second and then converting it using the standard conversion factor.
Step 2: Key Formula or Approach:
1. Total Distance (\(D\)) = Length of Train (\(L_t\)) + Length of Platform (\(L_p\))
2. Speed (\(S\)) = \( \frac{\text{Distance}}{\text{Time}} \)
3. Conversion Factor: To convert m/s to km/h, multiply by \( \frac{18}{5} \).
Step 3: Detailed Explanation:
Let's analyze the given numerical data:
Length of the train (\(L_t\)) = 180 m
Length of the platform (\(L_p\)) = 320 m
Time taken (\(T\)) = 25 seconds
First, we establish the total path length:
\[ \text{Total Distance} = 180 \text{ m} + 320 \text{ m} = 500 \text{ meters} \]
Now, we calculate the speed of the train in the metric units of meters per second (m/s):
\[ \text{Speed} = \frac{500}{25} \]
Dividing 500 by 25:
\[ \text{Speed} = 20 \text{ m/s} \]
The final requirement is to present the answer in km/h.
The logic for conversion is that 1 km = 1000 m and 1 hour = 3600 seconds.
Thus, \( 1 \text{ m/s} = \frac{3600}{1000} \text{ km/h} = \frac{18}{5} \text{ km/h} \).
Applying this to our result:
\[ \text{Speed (in km/h)} = 20 \times \frac{18}{5} \]
Divide 20 by 5 to get 4:
\[ \text{Speed} = 4 \times 18 \]
\[ \text{Speed} = 72 \text{ km/h} \]
Step 4: Final Answer:
The speed of the train is 72 km/h.