Two particles A and B get 4m closer each second while traveling in opposite direction They get 0.4 m closer every second while traveling in same direction. The speeds of A and B are respectively :

Options

A. ` 2.2 ms ^(-1) and 0 A ms^(-1)`
B. ` 2.2 ms ^(-1) and 1.8ms ^(-1)`
C. ` 4 ms ^(-1 ) and 0 A ms ^(-1) `
D. None of these

Explanation

To solve the problem, we need to find the speeds of particles A and B, given their relative speeds when traveling in opposite and same directions.

### Step-by-Step Solution:

1. **Understanding Relative Velocity**:
- When two particles A and B are moving in opposite directions, their relative velocity is the sum of their speeds:
\[ V_A + V_B = 4 \text{ m/s} \]
- When they are moving in the same direction, their relative velocity is the difference of their speeds:
\[ V_A - V_B = 0.4 \text{ m/s} \]

2. **Setting Up the Equations**:
- From the first condition (opposite direction):
\[ V_A + V_B = 4 \quad \text{(1)} \]
- From the second condition (same direction):
\[ V_A - V_B = 0.4 \quad \text{(2)} \]

3. **Adding the Equations**:
- To eliminate \( V_B \), we can add equations (1) and (2):
\[ (V_A + V_B) + (V_A - V_B) = 4 + 0.4 \]
\[ 2V_A = 4.4 \]
\[ V_A = \frac{4.4}{2} = 2.2 \text{ m/s} \]

4. **Substituting to Find \( V_B \)**:
- Now, substitute \( V_A \) back into equation (1) to find \( V_B \):
\[ 2.2 + V_B = 4 \]
\[ V_B = 4 - 2.2 = 1.8 \text{ m/s} \]

5. **Final Speeds**:
- The speeds of particles A and B are:
\[ V_A = 2.2 \text{ m/s}, \quad V_B = 1.8 \text{ m/s} \]

### Conclusion:
The speeds of particles A and B are \( V_A = 2.2 \text{ m/s} \) and \( V_B = 1.8 \text{ m/s} \), respectively.

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