The paper studies a system of quasi-linear hyperbolic equations that describe a stationary planar hypersonic flow of dissociated gas. The speed of propagation of the acceleration wave was determined, and the problem of the rise and fall of the wave was solved analytically. The critical moment was determined when the acceleration wave breaks up into a shock wave due to the non-linear increase in slope. The global behavior of the wave amplitude was investigated and some interesting results were obtained.