The velocities of 5 molecules are `2m//s,3m//s,4m//s,5m//s and 6m//s` respectively. What is their mean velocity?

Options

A. `2m//s`
B. `3m//s`
C. `4m//s`
D. `7m//s`

Explanation

To find the mean velocity of the 5 molecules with given velocities, we can follow these steps:

### Step-by-Step Solution:

1. **List the Velocities**: The velocities of the molecules are given as:
- \( V_1 = 2 \, \text{m/s} \)
- \( V_2 = 3 \, \text{m/s} \)
- \( V_3 = 4 \, \text{m/s} \)
- \( V_4 = 5 \, \text{m/s} \)
- \( V_5 = 6 \, \text{m/s} \)

2. **Sum the Velocities**: To find the mean velocity, we first need to calculate the total sum of these velocities:
\[ \text{Total Sum} = V_1 + V_2 + V_3 + V_4 + V_5 \]
\[ = 2 + 3 + 4 + 5 + 6 \]

3. **Calculate the Total Sum**:
- Adding the velocities step-by-step:
- \( 2 + 3 = 5 \)
- \( 5 + 4 = 9 \)
- \( 9 + 5 = 14 \)
- \( 14 + 6 = 20 \)
- Thus, the total sum of the velocities is \( 20 \, \text{m/s} \).

4. **Count the Number of Velocities**: The total number of velocities is 5.

5. **Calculate the Mean Velocity**: The mean velocity (\( V_{\text{mean}} \)) is calculated by dividing the total sum of the velocities by the number of velocities:
\[ V_{\text{mean}} = \frac{\text{Total Sum}}{\text{Number of Velocities}} = \frac{20}{5} \]

6. **Final Calculation**:
\[ V_{\text{mean}} = 4 \, \text{m/s} \]

### Conclusion:
The mean velocity of the 5 molecules is \( 4 \, \text{m/s} \).

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