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Speed
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Relativistic Considerations
In Special Relativity, the concept of speed requires careful treatment because measurements of time and distance are relative to the observer's inertial frame. While the speed of light $c$ is invariant across all inertial frames, the observed speed of massive objects is governed by the relativistic velocity addition formula. Furthermore, the [proper accele… -
Velocity
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Relativistic Considerations
In special relativity, the classical definition of velocity must be modified due to the constancy of the speed of light ($c$). The relativistic velocity addition formula ensures that the resultant velocity never exceeds $c$.
If an object has velocity $\mathbf{u}$ relative to a frame $S'$, and $S'$ has a velocity $\mathbf{v}$ relative to frame $S$, the resulting velocity $\mathbf{u}'$ observed in $S$ is: