# How can we relate the particles motion in $k$-space to $x$-space?

Suppose a particle's time evolution in a 2D $$k$$-space of first Brillouin zone is as shown in the figure. How can we interpret the motion of the particle in $$x$$-space?

Any hint for interpretation is useful for me.

In general, to relate velocity and real space motion you need to integrate $$\vec x(t) = \int_{\rm t_0}^{\rm t} \, dt' \, \vec v(t) \equiv \vec x(t) = \int_{\rm t_0}^{\rm t} \, dt' \, \vec v((k(t)).$$