Great importance is attached to physical exercise and students' cognitive development, yet the precise mechanism linking the time duration of physical activities or sports with adolescents' cognitive development remains inconclusive. Based on the two-wave panel data of China Education Panel Survey (CEPS), this paper empirically examines the impact of daily physical exercise duration on junior middle school students' cognitive abilities, by using the two-way fixed-effect estimation. The findings reveal a nonlinear relationship, specifically an inverted "U"-shaped pattern, between daily time length of physical activities or sports and students' cognitive performance. The cognitive benefits of time investment in physical activities or sports reach the peak at approximately 0.829 h (equivalent to 50 min) per day among the teenagers in China. Furthermore, the daily time allocated to physical activities or sports affects students' cognitive performance differentially, students attending rural schools were rewarded more progressively, students of poorer physical fitness and those in good shape did not show discernible between-group differences. This study shades light on educational governance and time management, urging school administrators, parents and students to optimize the efficiency and utility of time resource invested in sports activities.
Keywords Time duration of physical activities or sports, Cognitive abilities, Time economics, Nonlinear effect of time resourcePhysical activity is one of the most beneficial means of bolstering individuals' physical fitness 1,2 , immune system 3 and cognitive capacities 4,5 . It is so important for the human beings that the World Health Organization (WHO) had embarked on an ambitious initiative titled "More Active People for a Healthier World, " a concerted effort focused on promoting physical activity 6 . This action plan strives to mitigate 15% of the global prevalence of insufficient physical activity among adolescents and adults by the year 2030, and recommends adolescents to do "60 minutes of moderate-to vigorous-intensity activity daily".Extensively documented, it emerges as a pivotal contributor to modifying brain structure, and thus enhancing cognitive function 7 . Neuropsychologists have intensively examined this phenomenon and accumulated a wealth of knowledge in this field [8][9][10] . For instance, they argue that the hippocampus region which is the central hub governing memory processes (including storage, conversion, retrieval), neural plasticity and learning capacity, special cognition and navigation, emotional regulation et al., is significantly impacted by regular physical activities or sports [11][12][13][14] .The positive association between physical activities and cognitive development is largely attributed to the release of brain-nourishing chemicals during sports exercise or physical exertion 15,16 . For instance, neuroscientist Wendy Suzuki's insightful TED talk in 2017, "The brain-changing benefits of exercise", highlighted that physical activity ele...