In this first work attempts to analytically explain the effects on the magnetic braking index, $q$, caused by the evolution of stellar velocity in main-sequence stars, and estimated by de Freitas & De Medeiros (2013). We have found that the effect of $q$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars as a function of the mass of stars. We note that our models predict that the calculated ages are distinct from gyrochronology ages. Indeed, the gyro-ages are measured considering only the canonical value of the Skumanich relation ($q$=3). As a result, we find that the age of stars can be well-determined when $q$ is free parameter. We also verified that for rotation periods less than $sim$ 5 days (i.e., fast rotators) there is a strong discrepancy among the different indexes $q$. In addition, the ages measured by gyrochronology model can be underestimated according to mass range selected. In conclusion, we suggest that the generalized gyro-ages by magnetic braking index can be an interesting way to better understand the idea of rotation as a clock.
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