A recent study investigated the effects of regular exercise on cognitive function. In an experimental condition, students took part in a regular exercise program for four weeks before completing cognitive and affective tests.
The researchers found that indeed, a mere 30 minutes of physical exercise once a day for the period preceding the tests was enough to produce measurable benefits to both cognition and perceived levels of anxiety. For this to work, though, exercise needs to be regular; exercising only on the day of the test did not produce the same benefits. The key is regularity rather than intensity.
When I started swimming (semi-)regularly last year I was better able to recall new French vocabulary I was learning at the time. The study assessed novel object recognition memory (NOR). This involved showing participants a set of objects before the 4-week block and afterwards. Those who completed the physical exercise showed improved performance in recognising which objects they had seen 4 weeks earlier.
Other studies have provided evidence of positive benefits to attention, decision-making, and mental health. The question is whether exercise benefits other kinds of memory. Object recognition can be applied to words. Written words are objects with a particular shape and character, so it stands to reason that improved object recognition would translate to written word recognition.