Explanation:

- The velocity of the center of mass can be found using the formula for the center of mass velocity of a system: \( V_{\text{cm}} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2} \).

- Since the particles are identical, \( m_1 = m_2 \).

- Let’s assign the particles: particle 1 has velocity \( v_1 = 2v \) and particle 2 has velocity \( v_2 = -v \) (negative because they move towards each other).

- Substituting in the equation:

$$ V_{\text{cm}} = \frac{m(2v) + m(-v)}{m + m} = \frac{2mv - mv}{2m} = \frac{mv}{2m} = \frac{v}{2} $$

- Option 3: \( \frac{v}{2} \) is the correct answer.

YOUR ANSWER IS RIGHT.