The visual environment contains many objects, yet only a few of them are behaviourally relevant. How we find relevant objects is a longstanding question in cognitive psychology. Research on selective visual attention has made tremendous progress in this area over the last forty years or so, underpinned by the visual search paradigm. In a visual search task, participants are asked to find a target among non-target objects on a computer screen. It is now well established that a set of basic visual features are initially extracted, prior to further scene analysis for relevant objects. Importantly, the accuracy of target-selection in visual experiments is subject to speed-accuracy trade-off (SAT), i.e. we are more likely to miss a target if we respond quickly. We exert a high degree of control over this trade-off, i.e. whether we favour speed over accuracy or vice versa, depending on our motivation. Such flexibility is believed to have been important for human survival, but nonetheless, little research has been conducted on how this control is exerted over visual search, much less its neural bases. With a focus on motion stimuli, we set out to develop a computational model of cognitive control for visual search, and to test the model's predictions for neural activity and behaviour under speed and accuracy emphasis.