Final answer:
The rate at which the distance between two moving cars changes can be calculated using the Pythagorean theorem and kinematics. When two cars collide and stick together, the center-of-mass velocity remains constant due to momentum conservation. The relative velocity of one moving object with respect to another can be found using vector subtraction.
Step-by-step explanation:
Given two cars in motion, one travelling east and the other travelling north, the rate at which the distance between them changes can be calculated using the Pythagorean theorem to represent the direct distance as a function of the east-west (x) and north-south (y) distances. If the car travelling west slows down, while the car heading south speeds up, the change in total momentum would be affected by these changes in velocity, though total momentum is conserved if no external forces are acting.
In a scenario where two cars collide and stick together, the center-of-mass velocity would remain the same before and after the collision due to the conservation of momentum. The velocities and directions of each car need to be combined using vector addition to determine the velocity of the center-of-mass both before and after the collision.
The relative velocity of a car in relation to a truck is another example of determining changes in a system of moving bodies. The relative velocity can be found by taking the vector difference of the two vehicles' velocities. All these concepts fall under the study of kinematics, which is part of classical mechanics in Physics, addressing the motion of objects without considering the forces that cause the motion.