Movimiento Rectilíneo Uniforme

Two Frames of Reference, One with Constant Velocity

• Two reference frames, one stationary and the other moving at a constant velocity, can describe the same displacement for a particle's motion.
• This is due to the principle of relativity, which states that the laws of physics are the same for all observers in uniform motion.
• The key is that the relative velocity between the two frames is constant.
• If the observer in the moving frame measures a displacement, the stationary observer will measure a different displacement, but in both contexts the path is the same.

Displacement

• Displacement is a vector quantity that describes the change in position of an object.
• It is defined as the straight-line distance between the initial and final positions of an object.
• A particle's displacement in one frame of reference can be computed as the final vector subtracted from the initial position.

Constant Velocity Motion (MRU)

• Motion with uniform velocity (MRU) means that an object's speed and direction remain constant.
• The velocity vector doesn't change over time. This leads to the direct relationship between displacement, velocity, and time in a single frame of reference.

Relating Displacement in Different Frames

• When a particle moves in a constant velocity frame, the stationary observer will observe a different displacement profile. The relative velocity between frames will result in a shift in the position vector between the observers. However, the overall path of the particle would be the same.
• Consider a particle moving at a constant velocity in frame B, which (B) is moving with constant velocity relative to frame A. This combination would imply a different description of the particles' motion in the observer of frame A. The observer in frame A will measure a different displacement due to the combined translational velocity.

Implications of the Principle of Relativity

• The principle of relativity asserts that the laws of physics are invariant (remain the same) in all inertial frames of reference. This is a crucial concept.
• Consequently, two observers in uniformly moving frames will observe the different effects of motion on the particle.
• This principle emphasizes that there is no 'absolute' frame of reference from which to view observations of motion.

Summary

• Two observers, one stationary and one moving uniformly, can obtain different descriptions of a particle's motion.
• These differences are due to the relative motion between the frames of reference.
• The key concept is that these different descriptions can still yield the same final displacement of the particle.
• The principle of relativity states that the physics remain the same in both frames.