How is the speed of an object related to an inertial observer moving with relative speed v?

The relationship between the speed of an object and an inertial observer moving with a relative speed ( v ) is described by the principles of special relativity, specifically the velocity addition formula. The correct choice, u = (u - v)/(1 - uv/c²), captures how velocities combine when considering relativistic effects, particularly when the speeds involved are close to the speed of light, ( c ).

This formula is essential because, in classical mechanics, velocities could simply be added or subtracted. However, as speeds approach the speed of light, time dilation and length contraction come into play, necessitating a more complex relationship. In the formula, ( u ) represents the velocity of the object as measured in one inertial frame, while ( v ) is the relative velocity of another inertial observer. The adjustments made for the relativistic effects ensure that the resultant velocity never exceeds ( c ), maintaining the fundamental postulate of relativity.

The other options do not accurately reflect the principles of relativity. For instance, simple addition or subtraction of velocities fails to account for the relativistic effects important at high speeds. Therefore, the correct answer effectively incorporates these concepts, illustrating the complexity needed when dealing with relative motion in a relativistic