An apparatus for estimating a rate-of-penetration of a drill bit is provided, which in one embodiment includes a first sensor positioned on a drill bit configured to provide a first measurement of a parameter at a selected location in a formation at a first time, and a second sensor positioned spaced a selected distance from the first sensor to provide a second measurement of the parameter at the selected location at a second time when the drill bit travels downhole. The apparatus may also include a processor configured to estimate the rate-of-penetration using the selected distance and the first and second times.