The speed of wind during a storm is`10^5` mm per sec. How long (in seconds) will it take a dust particle suspended in air to travel 1km?

Options

A. 1
B. 0.1
C. 10
D. 0.01

Answer

To solve the problem, we need to determine how long it will take a dust particle to travel 1 kilometer at a wind speed of \(10^5\) mm/s.

### Step-by-step Solution:

1. **Convert Distance from Kilometers to Millimeters**:
- We know that \(1 \text{ km} = 1000 \text{ m}\).
- Since \(1 \text{ m} = 1000 \text{ mm}\), we can convert kilometers to millimeters:
\[ 1 \text{ km} = 1000 \text{ m} \times 1000 \text{ mm/m} = 1,000,000 \text{ mm} \]
- Therefore, the distance \(D = 1,000,000 \text{ mm}\).

2. **Use the Formula for Time**:
- The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Rearranging the formula to find time gives us:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

3. **Substitute the Values**:
- We have the distance \(D = 1,000,000 \text{ mm}\) and the speed \(S = 10^5 \text{ mm/s}\).
- Plugging in these values:
\[ \text{Time} = \frac{1,000,000 \text{ mm}}{10^5 \text{ mm/s}} \]

4. **Calculate the Time**:
- Simplifying the expression:
\[ \text{Time} = \frac{1,000,000}{100,000} = 10 \text{ seconds} \]

### Final Answer:
The time it will take for a dust particle to travel 1 kilometer at a wind speed of \(10^5\) mm/s is **10 seconds**.