One method of monitoring a formation core during coring operations can include measuring resistivities of a formation internal and external to a core barrel assembly, comparing the resistivities of the formation internal and external to the core barrel assembly, and determining a displacement of the core into the core barrel assembly, based at least in part on the comparing, while the core is being cut. A formation core analysis system can include multiple longitudinally spaced apart sets of transmitters and receivers which measure resistivity of a core while the core displaces into a core barrel assembly, and multiple longitudinally spaced apart sets of transmitters and receivers which measure resistivity of a formation external to the core barrel assembly while a coring bit penetrates the formation. A speed of displacement of the core may be indicated by differences in time between measurements taken via the different sets as the core displaces.