Final answer:
The question pertains to high school-level Physics, specifically dynamics and momentum of two masses on a frictionless surface and their interaction through a collision. It involves calculating changes in velocities and applying the conservation of momentum principle to solve for the center-of-mass velocity of a system after a collision.
Step-by-step explanation:
The subject of the question revolves around the concepts of dynamics, momentum, and collisions in classical mechanics, which is a part of Physics. Specifically, the questions deal with the motion of two masses on a frictionless surface and how they interact through a collision. One question involves an initial velocity and a collision leading to the masses sticking together, requiring the use of conservation of momentum to solve. Another question describes a block being pulled over a frictionless, massless pulley, which involves calculating the acceleration of the system and the tension in the string. These problems are typically encountered at the High School level, particularly in introductory physics courses.
For the scenario where mass A (1.0 kg) slides across a frictionless surface and collides with mass B (3.0 kg), the center-of-mass velocity of the system will change due to the collision. To find this change, one would apply the principle of conservation of momentum. Prior to the collision, only mass A has a velocity, so the total momentum is simply the product of mass A's mass and velocity. After the collision, the total momentum is shared by both masses as they move together with a new velocity. The change in the center-of-mass velocity can be calculated by comparing the system's momentum before and after the collision.