A train crosses a pole in 12 s, when it is traveling at 54 km/h. Find the length of the train.

Answer

To find the length of the train that crosses a pole in 12 seconds while traveling at a speed of 54 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 as 54 km/h. To convert this to meters per second (m/s), we use the conversion factor:
1 km/h = (1000 meters) / (3600 seconds) = 1/3.6 m/s.

Now, we can convert 54 km/h to m/s:
\[ \text{Speed in m/s} = 54 \times \frac{1000}{3600} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 2: Use the formula for distance
The distance (which is the length of the train) can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 3: Substitute the values into the formula
We know the speed of the train is 15 m/s and the time taken to cross the pole is 12 seconds. Now we can substitute these values into the formula:
\[ \text{Length of the train} = 15 \text{ m/s} \times 12 \text{ s} = 180 \text{ meters} \]

### Conclusion
The length of the train is 180 meters.

---