In what time will a train 100 metres long cross an electric pole, if its speed be 144km/hour?

Options

A. 2.5 seconds
B. 5 seconds
C. 12.5 seconds
D. `3(5)/(4)` seconds

Answer

To solve the problem of how long it will take for a train 100 meters long to cross an electric pole at a speed of 144 km/h, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the train is given in kilometers per hour (km/h), and we need to convert it to meters per second (m/s) because the length of the train is given in meters.

1 km = 1000 meters
1 hour = 3600 seconds

To convert km/h to m/s, we use the formula:
\[ \text{Speed in m/s} = \left(\text{Speed in km/h} \times \frac{1000 \text{ m}}{1 \text{ km}}\right) \div \left(\frac{3600 \text{ s}}{1 \text{ hour}}\right) \]

Substituting the speed:
\[ \text{Speed in m/s} = \left(144 \times \frac{1000}{3600}\right) = \left(144 \times \frac{5}{18}\right) = 40 \text{ m/s} \]

### Step 2: Calculate the time taken to cross the electric pole
The time taken to cross an object (in this case, the electric pole) can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Here, the distance is the length of the train (100 meters) and the speed is 40 m/s.

Substituting the values:
\[ \text{Time} = \frac{100 \text{ m}}{40 \text{ m/s}} = 2.5 \text{ seconds} \]

### Conclusion
The train will take 2.5 seconds to cross the electric pole.

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