An analytical solution of the basic coupled stimulated Brillouin scattering (SBS) equations is obtained which describes the evolution of a Stokes pulse injected into an extended Brillouin medium excited by CW pump radiation. We show that regardless of the pulse length of the input Stokes pulse the delay of the output Stokes pulse results entirely from the inertia of the acoustic wave excitation via the electrostrictive interaction of the Stokes pulse with CW pump radiation. This delay is the SBS build up time and not the SBS induced group delay normally attributed to slow light.