|Current high-resolution observations as well as advanced numerical simulations are continuously increasing our knowledge about the physics of formation and evolution of jets in the solar atmosphere. Understanding of the initiation as well as acceleration mechanisms of these solar jets are very crucial aspects. In the present work, we have studied an active-region (AR) jet that is triggered on 21 July 2013 in AR 11793. Using observations from IRIS, AIA/SDO and EIS/Hinode, we have studied the relationship between hot and cool components and their evolution. The complete dynamics of this jet shows a very different evolution of the hot and cool components. Spectroscopic observations of C II 1334.532~\AA\ line reveal rotating nature of the cool plasma and show the dominance of the double-peak profiles near the base of jet. This is suggestive of heating of hot plasma at the base of jet. Our analysis further suggests that the cool jet is triggered at due to the magnetic reconnection between emerging magnetic bi-pole and the preexisting magnetic field and is accelerated through the slingshot effect of magnetic field lines. Hot component of the jet is formed later on due to the chromospheric evaporation that is initiated earlier by the magnetic reconnection. A time as well as spatial difference has been found in the triggering of cool and hot jets.