Galaxy properties are known to correlate most tightly with the galaxy effective stellar velocity dispersion {sigma}_e_. Here, we look for additional trends at fixed {sigma}_e_ using 1339 galaxies (M_*_>~6x10^9^M_{sun}_) with different morphologies in the MaNGA (DR14) sample with integral-field spectroscopy data. We focus on the gradients ({gamma}_rms_={sigma}(R_e_/4)/{sigma}_e_) of the stellar root-mean-square velocity (V_rms_=sqrt(V^2^+{sigma}^2^)), which we show traces the total mass density gradient {gamma}_tot_ derived from dynamical models and, more weakly, the bulge fraction. We confirm that {gamma}_rms_ increases with {sigma}_e_, age, and metallicity. We additionally find that these correlations still exist at fixed {sigma}_e_, where galaxies with larger {gamma}_rms_ are found to be older and more metal-rich. It means that mass density gradients contain information of the stellar population which is not fully accounted for by {sigma}_e_. This result puts an extra constraint on our understanding of galaxy quenching. We compare our results with galaxies in the IllustrisTNG hydrodynamical simulations and find that, at fixed {sigma}_e_, similar trends exist with age, the bulge fraction, and the total mass density slope but, unlike observations, no correlation with metallicity can be detected in the simulations.