A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive accessibility rule," namely that alternative explanations are considered less frequently when an explanation with relatively high accessibility is offered first. In a series of four experiments, we test the cognitive accessibility rule in the context of consideration of alternative explanations for six physical scenarios commonly found in introductory physics curricula. First, we administer free recall and recognition tasks to operationally establish and distinguish between the relative accessibility and availability of common explanations for the physical scenarios. Then, we offer either high or low accessibility explanations for the physical scenarios and determine the extent to which students consider alternatives to the given explanations. We find two main results consistent across algebra- and calculus-based university level introductory physics students for multiple answer formats. First, we find evidence that, at least for some contexts, most explanatory factors are cognitively available to students but not cognitively accessible. Second, we empirically verify the cognitive accessibility rule and demonstrate that the rule is strongly predictive, accounting for up to 70% of the variance of the average student consideration of alternative explanations across scenarios. Overall, we find that cognitive accessibility can help to explain biases in the consideration of alternatives in reasoning about simple physical scenarios, and these findings lend support to the growing number of science education studies demonstrating that tasks relevant to science education curricula often involve rapid, automatic, and potentially predictable processes and outcomes.