Adding two velocities v and w (in 1 dimension) in the relativistic mechanics needs to be done with the following formula:
$$v\oplus w = \frac{v+w}{1+vw}$$
The speed of light is assumed c=1. The interval $(-1,1)$ together with $\oplus$ forms a group. Here is an example of such "addition":
$$\frac{1}{2}\oplus\frac{1}{2}= \frac{1/2 + 1/2}{ 1+\frac{1}{2}\frac{1}{2}} = \frac{4}{5} $$
The following diagram is sort of a slide rule for space travelers (like Ijon Tichy).
The horizontal line is the real axis for the values of velocities.
Point labelled "v+w" in the figure represents the relativistic sum of velocities v and w. Move "v" or "w" to see how the result changes.
You may even experiment with tachyons! Slide velocity v to a value greater than 1 and see how adding a small velocity w slows it down.
For more see this.
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