Crossing a Platform
When a train passes an extended object like a station platform, bridge, or tunnel, the object's length cannot be ignored. To clear the structure completely, the train must travel a total distance equal to the sum of its own length plus the length of that structure.
Fundamental Principles
Compound Distance Sum
The absolute distance metric used when crossing extended stationary structures, defined as: $\text{Total Distance} = \text{Length of Train} + \text{Length of Platform}$.
Essential Formulation Tips
- The base formula for extended crossings is written as: $\text{Length of Train} + \text{Length of Platform} = \text{Speed} \times \text{Time}$.
- Be careful not to mix up the train's length with the platform's length when evaluating partial clues.
Shortcut Execution Techniques
- The Difference Extraction Shortcut: If a train passes a pole in 10 seconds and a 200-meter platform in 20 seconds, the extra 10 seconds are spent solely covering the 200-meter platform length. This allows you to find the speed instantly: $200 \text{ m} \div 10 \text{ s} = 20 \text{ m/s}$.
Contextual Inquiries (FAQs)
Q: Why do we add both lengths together instead of just using the platform's size?
A: Because a train is only considered completely past a platform once its very last car has cleared the exit edge, requiring it to travel its own length in addition to the platform's distance.
Example Breakdown: Calculating Platform Clearance Durations
Standard extended stationary target calculation.Calculate total compound distance: $\text{Distance} = \text{Train Length} (200\text{m}) + \text{Platform Length} (300\text{m}) = 500 \text{ meters}$.
Convert speed to m/s: $90 \times \frac{5}{18} = 5 \times 5 = 25 \text{ m/s}$.
Set up the crossing equation: $\text{Total Distance} = \text{Speed} \times \text{Time}$
Substitute values: $500 = 25 \times \text{Time}$.
Solve for time: $\text{Time} = \frac{500}{25} = 20 \text{ seconds}$.
Conclusion: The train clears the platform in 20 seconds.
Platform and Bridge Crossings
Practice managing combined lengths across bridges, tunnels, and station platforms.
Q1. A train passes a 120-meter long platform in 15 seconds while traveling at a speed of 72 km/h. Find the length of the train.