A radio transmitter which is accelerating with a non-zero radial component with respect to a receiver will produce a signal that appears to change its frequency over time. This effect, commonly produced in astrophysical situations where orbital and rotational motions are ubiquitous, is called a drift rate... In radio SETI (Search for Extraterrestrial Intelligence) research, it is unknown a priori which frequency a signal is being sent at, or even if there will be any drift rate at all besides motions within the solar system. Therefore a range of potential drift rates need to be individually searched, and a maximum drift rate needs to be chosen. The middle of this range is zero, indicating no acceleration, but the absolute value for the limits remains unconstrained. A balance must be struck between computational time and the possibility of excluding a signal from an ETI. In this work, we examine physical considerations that constrain a maximum drift rate and highlight the importance of this problem in any narrowband SETI search. We determine that a normalized drift rate of 200 nHz (eg. 200 Hz/s at 1 GHz) is a generous, physically motivated guideline for the maximum drift rate that should be applied to future narrowband SETI projects if computational capabilities permit. (read more)