There is a longstanding definition of instantaneous velocity. It saysthat the velocity at t 0 of an object moving along a coordinate line is r if and only if the value of the first derivative of the object's position function at t 0 is r. The goal of this paper is to determine to what extent this definition successfully underpins a standard account of motion at an instant. Counterexamples proposed by Michael Tooley (1988) and also by John Bigelow and Robert (...) Pargetter (1990) are reinforced and illuminated by considering the presence or absence of changes to the object's motion. (shrink)