We present new radial velocity measurements for 82 stars, members of the Galactic globular cluster NGC 6388, obtained from ESO-VLT KMOS spectra acquired during the instrument Science Verification. The accuracy of the wavelength calibration is discussed and a number of tests of the KMOS response are presented. The cluster systemic velocity obtained (81.3 +/- 1.5 km/sec) is in very good agreement with previous determinations. While a hint of ordered rotation is found between 9 and 20 from the cluster centre, where the distribution of radial velocities is clearly bimodal, more data are needed before drawing any firm conclusions. The acquired sample of radial velocities has been also used to determine the cluster velocity dispersion profile between ~9 and 70, supplementing previous measurements at r < 2 and r > 60 obtained with ESO-SINFONI and ESO-FLAMES spectroscopy, respectively. The new portion of the velocity dispersion profile nicely matches the previous ones, better defining the knee of the distribution. The present work clearly shows the effectiveness of a deployable Integral Field Unit in measuring the radial velocities of individual stars for determining the velocity dispersion profile of Galactic globular clusters. It represents the pilot project for an ongoing large program with KMOS and FLAMES at the ESO-VLT, aimed at determining the next generation of velocity dispersion and rotation profiles for a representative sample of globular clusters.
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