Optimizing a character build for ridiculous Movement in order to break the sound barrier or even the speed of light is a well-tried source of fun with numbers in DnD. Such speed optimizations usually incorporate lots of magic and possibly additional help by allies. But I'd like to learn more about what the human body is capable of within the rules of DnD, so I'm more interested in what can be achieved without magic.
A high level Monk with two levels in Fighter and the Mobile Feat can still become ridiculously fast. If I didn't mess up the calculations, they can run 100m in less than 7.4 seconds (see my answer below). This is even 2 seconds faster than 9.4s, which scientists think is the human limit (in our world, that is). But hey, it's a Level 20 character, so becoming somewhat superhuman does kind of make sense in the world of DnD, I guess.
This raises the question: At what point in the game can human adventurers become superhuman without using magic? This is of course a more vague and general question (one could ask the same e.g. in the context of lifting strength), but let's stick to running speed for the moment. So, my question in precise terms is:
What is the minimum level at which a human player character can run 100m in less than 9.58 (or: 9.4) seconds and thus break the current world record (or: become superhuman)?
Contest Rules:
- The character is in a wide open field with no allies, enemies or other threats that are of any relevance to them. In particular, outside help is not allowed.
- The character simply wants to run 100m as fast as possible. Running as in putting one foot in front of the other on the ground. No jumping, no flying, no teleportation, no other shenanigans. Assuming the ground to be flat, there must exist a continuous curve in space that connects the plane that contains the starting line and is orthogonal to the ground with the plane containing the finishing line and orthogonal to the ground such that each point of this curve intersects with the body of the runner at some time. Usually, a straight line at the height of the runner's chest should be a possible choice.
- Setup rounds are allowed, but they must not depend on circumstances the character cannot influence.
- Assume that Movement translates into speed and that time is not limited to the discrete grid of full rounds. For example, a Movement of 60 feet per round corresponds to a speed of 10 feet (or 3.048 metres) per second, as a round represents 6 seconds. With this speed, you need roughly 33 seconds for 100m. Different Movement in different rounds is handled in the same way: If your first turn grants you a Movement of say 210 feet and your consecutive turns each only grant you 150 feet, you will move at 35 feet per second for 6 seconds and at 25 feet per second afterwards, meaning that you cross the 100m mark after
$$ 6+\frac{100-210\cdot0.3048}{25\cdot0.3048}\approx10.723 $$
seconds, where the factor 0.3048 comes from transferring feet into meters. - No magic, i.e. no spells/cantrips or magic items. Monk Features (including those that require Ki points) are allowed since they are not magic in terms of game mechanics, although they are described as "background magic" in flavour text. The same reasoning applies to any similar feature (such as the Barbarian's Totem Spirit or the Wizard's Bladesong).
- No epic boons.
- No UA (but any official rule book).
PS: This list of constraints was expanded and made more precise with the help of lots of clever and insightful comments and answers from other users. Some of the answers may no longer cover all of these conditions (but they explicitly say so anyway), but that does not make them the least bit less relevant or even interesting.
Best Answer
7 levels.
Variant Human (30ft) with Mobile Feat (+10ft) with 2 Monk levels (+10ft from Unarmored Movement, and Step of the Wind) + 3 Totem Barbarian levels (+15ft Elk Totem during Rage) + 2 Fighter Levels (Action Surge).
Mr. Bolt has to run 100m in 9.4/s, or 328ft in 9.4s, or 210ft/turn (average speed). His base speed is 50ft.
As a setup, Bolt rages to achieve 65ft base speed. On his first turn, Bolt can use his movement, Dash as an Action, Dash as a Step of the Wind bonus action, and Dash as an Action Surge, he has 65ft*4 of movement to use, and covers 260ft (68ft missing). He loses his rage since he did not attack anyone. On his second turn, he uses his movement, Dash as an Action, and Dash as a Step of the Wind bonus action (with his last Ki Point) for 50ft*3 for 150 additional feet. Since he only had to cover 68ft, he did so in 68/150*6=2.72s, for an incredible 328ft (100m) in 8.72 seconds.
Congratulations, Mr Bolt! No magical Wild Shapes were necessary, no help, and no invalid racial Feats (as in the accepted answer). Also no shenanigans with doing multiple Action Surges, or sustaining Rage without making attacks. If a prep round for activating Rage is not allowed, the Barbarian can be level 5 for Fast Movement and beats the world record in 8.93s (thanks to goodguy5 for the Elk tip). If the Barbarian is level 5 and can prep the Rage, he beats the record in 6.93s.
Addendum: a Tabaxi with half his levels can do the same with Feline Agility. Darn cats!