A train 180 metres long ius running at a speed of `90 km/h`. How long will it take to pass a post ?

Options

A. 8.2 secs
B. 7.8 secs
C. 8 secs
D. 7.2 secs

Answer

To solve the problem of how long it will take for a train 180 meters long to pass a post while traveling at a speed of 90 km/h, we can follow these steps:

### Step 1: Identify the given information
- Length of the train = 180 meters
- Speed of the train = 90 km/h

### Step 2: Convert the speed from km/h to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor:
1 km/h = (1000 meters) / (3600 seconds)

So, we can convert 90 km/h as follows:
\[ \text{Speed in m/s} = 90 \times \frac{1000}{3600} \]

### Step 3: Simplify the conversion
Calculating the above expression:
\[ \text{Speed in m/s} = 90 \times \frac{1000}{3600} = 90 \times \frac{1}{3.6} = 25 \text{ m/s} \]

### Step 4: Use the formula for time
The time taken to pass the post can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is the length of the train (180 meters) and the speed is 25 m/s.

### Step 5: Substitute the values into the formula
\[ \text{Time} = \frac{180 \text{ meters}}{25 \text{ m/s}} \]

### Step 6: Calculate the time
Now, we perform the division:
\[ \text{Time} = 7.2 \text{ seconds} \]

### Conclusion
Thus, the time taken for the train to pass the post is **7.2 seconds**.