I do not have children of my own. However those that I have watched (nieces, nephews) as they grew up they stopped vomiting at an early age except when sick. That early age being around about 1 year when they started eating baby food and got off the bottle. So I suspect that vomiting is not 'normal' and would imply illness. Exercise Induced Nausea can occur shortly after exercise has stopped as well as during exercise itself. It may be a symptom of either over exertion during exercise, or from too abruptly ending an exercise session. People engaged in high intensity exercise such as aerobics and bicycling have reported suffering from exercise induced nausea. However I would like to point out that this is either during or right after exercise. Not the next day. I would schedule an appointment with a doctor. 'Vomiting' is most likely only one symptom here and there are many causes of vomiting. Balance can play a roll, a simple eye movement test can reveal a lot (follow the pen/finger with the eyes). Heat exhaustion - or too much sweating can also play a roll, but usually this also affects hunger, and there is a higher thirst in the heat affected person. Electrolyte imbalance after exercise can be another issue. Electrolytes are loss through sweating, thus products like Gatorade has them to replenish what the body has lost. Salts can also be added to that list. So you see I'm already starting a long list with just two factors 'vomiting' and 'exercise'.