Observers reacted to the change in the movement of a random-dot field whose initial velocity, V0, was constant for a random period and then switched abruptly to another value, V1. The two movements, both horizontally oriented, were either in the same direction (speed increments or decrements), or in the opposite direction but equal in speed (direction reversals). One of the two velocities, V0 or V1, could be zero (motion onset and offset, respectively). In the range of speeds used, 0-16 deg/sec (dps), the mean reaction time (MRT) for a given value of V0 depended on magnitude of V1-V0 only: MRT approximately r+c(V0)/magnitude of V1-V0 beta, where beta = 2/3, r is a velocity-independent component of MRT, and c(V0) is a parameter whose value is constant for low values of V0 (0-4 dps), and increases beginning with some value of V0 between 4 and 8 dps. These and other data reviewed in the paper are accounted for by a model in which the time-position function of a moving target is encoded by mass activation of a network of Reichardt-type encoders. Motion-onset detection (V0 = 0) is achieved by weighted temporal summation of the outputs of this network, the weights assigned to activated encoders being proportional to their squared spatial spans. By means of a "subtractive normalization," the visual system effectively reduces the detection of velocity changes (a change from V0 to V1) to the detection of motion onset (a change from 0 to V1-V0). Subtractive normalization operates by readjustment of weights: the weights of all encoders are amplified or attenuated depending on their spatial spans, temporal spans, and the initial velocity V0. Assignment of weights and weighted temporal summation are thought of as special-purpose computations performed on the dynamic array of activations in the motion-encoding network, without affecting the activations themselves.