Speed depends on the observer, this is relativity. Definitely not time particles, but rather light showing when the moving thing passed point A and point B and the distance between A and B.
Speed can be measured directly, for some macro objects, using the Doppler shift of waves sent towards the moving object.
At speeds much lower than the speed of light, it’s simple – the change of location divided by the change of time.
I think the question is in part a relativity question, in that strange things happen when objects get closer to the speed of light. From our reference frame, it seems that the mass is getting bigger and bigger as the velocity gets that fast. Spacetime, space and time, gets warped by mass, and hence also gets affected if an object with mass goes really, really fast.
In terms of the particle question, we don’t know. For the last 100 years physicists have been trying to somehow make quantum physics and general relativity, and we’re not there yet. If there are particles involved they’re much too small to measure yet.
Just as yesterday and tomorrow are not particles, neither are the place where you are sitting and the location of the refrigerator in your kitchen. The time that it takes you to cross the distance between your chair and your refrigerator to go grab a drink is *speed*.
Speed is made from the relationship between time and position. Neither position, nor time are particles but are rather continuous axes in the expanse of spacetime.
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