Step 1: Understanding the Question:
We need to calculate the time taken by a train of a given length and speed to cross a stationary object of negligible length, like a pole.
Step 2: Key Formula or Approach:
The fundamental formula is: Time = \(\frac{\text{Distance}}{\text{Speed}}\).
When a train crosses a pole, the distance covered is equal to the length of the train itself.
It is crucial to ensure that all units are consistent (e.g., meters for distance and m/s for speed).
Step 3: Detailed Explanation:
1. Identify the Distance:
The distance the train needs to cover to completely cross the pole is its own length.
Distance = 150 m.
2. Convert the Speed:
The speed is given in km/hr, but the distance is in meters. We need to convert the speed to m/s.
To convert km/hr to m/s, we multiply by the factor \(\frac{5}{18}\).
Speed = \(54 \, \text{km/hr} \times \frac{5}{18} = 3 \times 5 = 15 \, \text{m/s}\).
3. Calculate the Time:
Now we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{150 \, \text{m}}{15 \, \text{m/s}} = 10 \, \text{seconds} \]
Step 4: Final Answer:
The train will take 10 seconds to cross the pole.