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In the realm of special relativity, adding velocities isn't as straightforward as simply adding numbers. When dealing with speeds approaching the speed of light, the classical mechanics approach doesn't work. Instead, we use Einstein's formula for velocity addition to ensure calculations remain consistent with the principles of relativity.

The formula used is:

• \(v = \frac{v1 + v2}{1 + \frac{v1 \cdot v2}{c^2}}\)

Here, \(v1\) and \(v2\) are the velocities of two objects as measured in a given reference frame, and \(v\) is the resultant velocity. This equation ensures that no matter how high the individual velocities are, the resulting velocity \(v\) will never exceed the speed of light \(c\).

Let's consider the case where two particles approach each other head-on. If they have the same speed in opposite directions—making one velocity the negative of the other—Einstein's formula still helps align their relative motion correctly according to special relativity.

Relative speed becomes essential when observing objects moving towards or away from each other, especially when dealing with high velocities near the speed of light. In special relativity, the concept of relative speed accounts for how quickly an object appears to move from the perspective of another object.

In the given scenario, two particles are moving towards each other with a relative speed of \(0.890c\). Understanding relative speed means recognizing that the direct addition of velocities seen in everyday experiences isn't applicable here. Instead, the speed as perceived between the particles requires the relativistic velocity addition formula to be applied to get an accurate measure.

Thus, even as the particles race towards one another, the perceived speed between them remains lower than \(c\), adhering to the rules of special relativity and ensuring that the combined speed doesn't exceed the speed of light.

The speed of light, denoted as \(c\), is a fundamental constant of physics, valued at approximately \(3 \times 10^8\) meters per second. In the world of special relativity, it serves as a cosmic speed limit, an unbeatable velocity that nothing with mass can reach or exceed.

Einstein revolutionized our understanding of motion with the insight that the speed of light remains constant in all inertial frames of reference, regardless of the motion of the light source or observer. This essence is embedded in the Lorentz transformations, which replace the Galilean ones used in classical mechanics.

In practical terms, when calculating situations involving high-speed entities, like particles in a collider, adhering to the speed of light as the ultimate speed ensures no law of physics is violated. It has profound implications for how velocities are combined, as seen with the velocity addition formula, and defines an entirely new way of interpreting how objects move and interact at high velocities in the universe.