A

Step 1: Understand Statement 1: It asserts that during a collision, if the masses of the particles remain constant, their linear velocities will change along the common normal direction. This is consistent with the principles of conservation of momentum, where the velocities of colliding bodies change due to the interaction.

Step 2: Understand Statement 2: It states that a pair of equal and opposite impulses act along the common normal direction during a collision. This is also true because, according to Newton's third law, for every action, there is an equal and opposite reaction. The impulses will also be equal and opposite when considering the forces exerted by the colliding particles.

Step 3: Analyze the relationship: Statement 1 discusses the change in velocities due to momentum conservation, while Statement 2 explains the underlying reason (impulses) which leads to those changes. Therefore, Statement 2 provides the correct explanation for Statement 1.

Conclusion: Both statements are true and Statement 2 correctly explains Statement 1. Hence, the correct answer is option A.