The correct answer is option 3: Both Newton`s second law of motion and Newton`s third law of motion.

Newton`s second law of motion states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In terms of a collision between particles, this means that the change in momentum of each particle is directly related to the net force acting on it. If the net force on a particle changes during a collision, its momentum will change as well. This law helps explain the change in momentum of individual particles during a collision.

Newton`s third law of motion states that for every action, there is an equal and opposite reaction. In the context of a collision between particles, this means that the forces exerted by the particles on each other are equal in magnitude and opposite in direction. As a result, the sum of the momenta of the particles before the collision is equal to the sum of the momenta after the collision. This law helps explain the conservation of momentum during a collision.

Therefore, both Newton`s second law of motion and Newton`s third law of motion are necessary to understand the conservation of momentum in a collision.