How do athletes qualify for the Olympics?
Through a combination of entry standards and quota places, and the system is more complicated than "be fast enough", varying substantially by sport.
The two main routes in athletics:
Entry standard. Achieving a published performance mark within a defined qualifying window. These standards are set deliberately hard, intended to fill roughly half the available places.
World ranking. The remaining places are filled by the highest-ranked athletes not already qualified, using a ranking system combining performance and the quality of competition. This exists because a pure standard disadvantages athletes without access to fast races.
National quotas cap participation. A country may enter a maximum of three athletes per individual event regardless of how many meet the standard — which is why some nations hold trials more competitive than the Olympics themselves in their strongest events.
How other sports differ:
Team sports qualify as nations through continental tournaments and qualifying competitions, with a fixed number of teams.
Combat sports use continental qualifying events and world rankings, with weight-category quotas.
Swimming uses entry standards with A and B cuts, plus relay places.
Sports with subjective judging, such as gymnastics, use world championship results to allocate national quotas, with the nation then selecting athletes.
Crucially, quota places usually belong to the country, not the athlete. An athlete may earn a place that the national federation then awards to someone else, which is a recurring source of dispute.
Universality places are allocated to ensure small nations can participate even without qualified athletes, which is why some competitors are far off the standard.
Host nation places are automatic in some sports.
Additional requirements: eligibility to represent the country, no active doping sanction, and selection by the National Olympic Committee, which retains discretion.
Rules change every cycle, so previous qualification routes are not a guide.