Finding the velocity of a bounded quark of a meson How would you compute the velocity of one of the quarks of a meson, when we have no reference to a reaction or a collision?
I initially thought we could use the conservation of energy and momentum to deal with it, however, how do we do it without a collision or a decay for example.
 A: Take for example the pions ($\pi^+$, $\pi^-$, $\pi^0$).
All three of them have a mass around $140\text{ MeV/c}^2$.
They consist of one quark ($u$ or $d$)
and one antiquark ($\bar{u}$ or $\bar{d}$).
The rest masses of these quarks are much smaller
(only $2$ or $5 \text{ MeV/c}^2$ respectively).
So you see, their masses contribute only
very little to the total mass of the pion.
Hence the pion mass is mostly from the kinetic energy
of the constituent quarks (and may be from the gluons also).
That means the quarks are
moving within the pion very close to the speed of light.

Another way to find the speed of a quark
is to start with the radius of the pion.
The article "Charge Radius of Pion" has published
a radius of $0.51 \cdot 10^{-15}$ m.
From Heisenberg's uncertainty relation you can then estimate
the momentum $p$ of a quark inside the pion as
$$p \geq \frac{\hbar}{r}
=\frac{6.6\cdot 10^{-16}\text{ eV s}}{0.51\cdot 10^{-15}\text{ m}}
=1.3\text{ eV s/m}
=390\text{ MeV}/c.$$
Then you can use the definition of relativistic momentum
$$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}},$$
resolve this to $v$ as a function of momentum $p$ and quark mass $m$,
$$v=c\frac{p}{\sqrt{p^2+m^2c^2}}.$$
Because of $p\gg mc$ you will again get a speed $v$ very close to $c$.
A: I am turning my comments into an answer in order to include a figure:
Quote from Motl's answer to a similar question, about electrons in an atom:

The state of an electron (or electrons) in the atoms isn't an eigenstate of the velocity (or speed) operator, so the speed isn't sharply determined. However, it's very interesting to make an order-of-magnitude estimate of the speed of electrons in the Hydrogen atom (and it's similar for other atoms).

That is why the electrons are in orbitals, not orbits. See  this link for details of the  measured orbitals of the Hydrogen atom,

There is no consecutive $Δs$ to a $Δt$ to be able to define a velocity.
On average is a different story, as discussed in the link by Motl

However, it's very interesting to make an order-of-magnitude estimate of the speed of electrons in the Hydrogen atom (and it's similar for other atoms).

In the strong interaction that binds the  quarks, a Bohr type model is impossible, all successful calculations have been done with QCD on the lattice, so there is not even a classical approximation to the orbitals of the quarks. The same general principles can be used to get average numbers , as in the link. To ask about a minimum velocity of a quark makes no sense, in my opinion.
