Question

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. determine whether the quantities below are the same or different when expressed in these two coordinate systems.

Answer 1

The choice of coordinate system does not affect the physical outcome of the motion between two points.

Step-by-step explanation:

When describing the motion of a particle from point A to point B, the choice of coordinate system can affect how quantities are expressed. However, the physical results remain the same regardless of the coordinate system chosen.

For example, if two observers are viewing the motion from different reference points, the quantities may be expressed differently in the two coordinate systems, but the physical outcome will be the same. The choice of coordinate system can make problem-solving easier, such as choosing an axis parallel to gravity in projectile motion.

It's important to note that while the choice of coordinate system may affect how an answer is written, it should not affect the underlying physics of the process.

Answer 2

The physical quantities describing the motion of a particle from A to B remain the same regardless of the coordinate system used, though the coordinates and trajectory descriptions differ with different origins.

Step-by-step explanation:

In the situation where a particle moves from point A to point B, the physical quantities such as displacement, velocity, and acceleration are invariant of the choice of coordinate system, provided that the systems are not in relative motion with respect to each other and that one is simply a translation of the other. However, the actual coordinates of the points A and B, as well as the particle's trajectory, will be different due to the different origins of the coordinate systems.

Scalar quantities, such as distance and speed, remain unaffected by the change in the origin. In contrast, vector quantities like displacement, velocity, and acceleration are described relative to the origin and thus will have different numerical values in each coordinate system, even though the physical situation they describe remains the same.

Choosing an axis parallel to key vectors in the problem, such as the initial velocity or an applied force, can simplify calculations but will not affect the physical outcome of the situation.