Question

A train travelling at 72 km/h crosses a pole in 15 seconds. The length of the train is:

• A. 250 m
• B. 280 m
• C. 300 m
• D. 320 m

Hint:

Keep these common speed metric equivalents handy to bypass calculation steps entirely during time-sensitive tests:
• $18 \text{ km/h} = 5 \text{ m/s}$
• $36 \text{ km/h} = 10 \text{ m/s}$
• $54 \text{ km/h} = 15 \text{ m/s}$
• $\mathbf{72 \text{ km/h} = 20 \text{ m/s}}$ Recognizing that $72 \text{ km/h}$ is exactly $20 \text{ m/s}$ lets you simply multiply $20 \times 15 = 300 \text{ m}$ instantly!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a moving train travels past a stationary point object of negligible width (such as a telegraph pole, a signal post, or a standing person), the total distance covered by the train during the crossing is exactly equal to its own physical length. Before calculating, we must ensure all measurement units are uniform by matching the speed units with the time units.

Step 2: Key Formula or Approach:
1. Convert Speed from $\text{km/h}$ to $\text{m/s}$: $$\text{Speed (m/s)} = \text{Speed (km/h)} \times \frac{5}{18}$$ 2. Distance formula: $$\text{Distance} = \text{Speed} \times \text{Time}$$ $$\text{Length of Train} = \text{Speed (m/s)} \times \text{Time (seconds)}$$

Step 3: Detailed Explanation:
Let's complete the calculations systematically: Step A: Uniform Unit Transformation The speed is given as $72 \text{ km/h}$ and the time duration is given in seconds. Let's convert the speed into meters per second ($\text{m/s}$): $$\text{Speed} = 72 \times \frac{5}{18} \text{ m/s}$$ Dividing $72$ by $18$ gives $4$: $$\text{Speed} = 4 \times 5 = 20 \text{ m/s}$$ Step B: Calculate Distance The train takes $15 \text{ seconds}$ to completely clear the pole traveling at this uniform velocity. Now calculate the total distance covered: $$\text{Distance} = \text{Speed} \times \text{Time}$$ $$\text{Distance} = 20 \text{ m/s} \times 15 \text{ s} = 300 \text{ meters}$$ Since the distance traveled to pass a single point equals the train's own span, the length of the train is $300 \text{ m}$. This corresponds perfectly to choice (c).

Step 4: Final Answer:
The length of the train is 300 m.