Find the maximum particle velocity for a wave described. by the equation y = A sin⁡(kx - ωt).

Given equation is equation of simple harmonic wave $y=A\sin (kx-\omega t)$

velocity, $v=\frac{dy}{dt}=A\omega \cos (kx-\omega t)$

Maximum value of cosine function is 1. All the Particles oscillate in SHM hence max. $\text{ velocity }=A\omega$