Final answer:
The position of the particle at point A differs in two coordinate systems with different origins, but the displacement from A to B remains the same in both systems because it is independent of the origin.
Step-by-step explanation:
Consider a physical situation in which a particle moves from point A to point B. This process is described from two coordinate systems that are identical except that they have different origins. The position of the particle at point A differs as expressed in one coordinate system compared to the other, but the displacement from A to B is the same as expressed in both coordinate systems.
To describe motion in physics, we often use a three-dimensional coordinate system with variables x(t), y(t), and z(t) which are functions of time. When defining motion, the initial position depends on the origin of the chosen coordinate system, which explains why the position at point A would differ between two coordinate systems with different origins. However, displacement, which is the straight-line distance from point A to point B, remains the same regardless of the origin of the coordinate system, as it's based on a change in position.
Choosing an appropriate coordinate system is essential for simplifying the mathematics involved in problem-solving, especially in cases such as projectile motion or when studying relative velocities and classical relativity. In these scenarios, it's often easier to select a coordinate system whose axes are parallel to the relevant velocities or forces, like gravity.