Angle-averaged radii (upper panel) and velocities (lower panel) of the forward (solid lines) and reverse (dashed lines) shocks vs. time for models assuming a different value of injection rate η (see legend in units of 10⁻⁴; see also Figure 2). The red crosses show the corresponding observational values at the current age of Cas A (see Table 1); the vertical lines of the crosses show the observational uncertainty.