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We present CaII K line chromospheric fluxes measured from high-resolution spectra in 35 G dwarf stars of 5 open clusters to determine the age-activity-rotation relationship from the young Hyades and Praesepe (0.6Gyr) to the old M 67 (∼4.5Gyr) through the two intermediate age clusters IC4651 and NGC3680 (∼1.7Gyr). The full amplitude of the activity index within a cluster is slightly above 60 % for all clusters but one, NGC 3680, in which only two stars were observed. As a comparison, the same Solar CaII index varies by ∼ 40 % during a solar cycle. Four of our clusters (Hyades and Praesepe, IC 4651 and NGC 3680) are pairs of twins as far as age is concerned; the Hyades have the same chromospheric-activity level as Praesepe, at odds with early claims based on X-ray observations. Both stars in NGC 3680 are indistinguishable, as far as chromospheric activity is concerned, from those in the coeval IC 4651. This is a validation of the existence of an age-activity relationship. On the other hand, the two intermediate age clusters have the same activity level as the much older M67 and the Sun. Our data therefore shows that a dramatic decrease in chromospheric activity takes place in solar stars between the Hyades and the IC 4651 age, of about 1Gyr. Afterwards, activity remains virtually constant for more than 3Gyr. We have also measured v sin i for all of our stars and the average rotational velocity shows the same trend as the chromospheric-activity index. We briefly investigate the impact of this result on the age determinations of field G dwarfs in the solar neighborhood; the two main conclusions are that a consistent group of ``young'' stars (i.e. as active as Hyades stars) is present, and that it is virtually impossible to give accurate chromospheric ages for stars older than ∼2Gyr. The observed abrupt decline in activity explains very well the Vaughan-Preston gap.