A train travelling at 90 km/h crosses a pole in 8 s. Find the length of the train (in m).

Options

A. 250
B. 200
C. 150
D. 178

Explanation

To find the length of the train that crosses a pole in 8 seconds while traveling at a speed of 90 km/h, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
To convert the speed from kilometers per hour (km/h) to meters per second (m/s), we use the conversion factor \( \frac{5}{18} \).

\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

Substituting the given speed:

\[ \text{Speed in m/s} = 90 \times \frac{5}{18} \]

### Step 2: Calculate the speed in m/s
Now we calculate:

\[ \text{Speed in m/s} = 90 \times \frac{5}{18} = 90 \times \frac{5}{18} = \frac{450}{18} = 25 \text{ m/s} \]

### Step 3: Use the formula for distance
The distance (length of the train) can be calculated using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 4: Substitute the values into the formula
We know the speed is 25 m/s and the time is 8 seconds. So we substitute these values into the formula:

\[ \text{Distance} = 25 \text{ m/s} \times 8 \text{ s} \]

### Step 5: Calculate the distance
Now we calculate the distance:

\[ \text{Distance} = 25 \times 8 = 200 \text{ meters} \]

### Conclusion
Therefore, the length of the train is **200 meters**.

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