How to go 100mph in D&D 5e

Step one: Play a tabaxi
Step two: Play a tabaxi monk all the way up to 19th level
Step three: Take the mobile feat at every ability score increase
Step four: Have somebody cast Haste on you
Step five: Become Sonic the Hedge…cat.
So here’s how this works. A tabaxi’s base speed is 30 feet, but they have the feline agility ability which means that they can go double speed as part of their normal movement but they have to be still for a round to recharge this ability, so you can only cat dash once a run.
So 30 feet of normal movement = 30 feet. Plus 30 feet of unarmored movement = 60 feet. Plus mobile five times is +50 feet = 110 feet of normal movement. Now double it with haste, and that’s 220 feet of movement.
220 feet normal movement + 220 feet feline agility + 220 feet dash action + 220 feet step of the wind bonus dash = 880 feet of movement in 6 seconds.
880ft/6s x 10 = 8800ft/1min x 60min/1hr = 528000ft/1hr ÷ 5280ft/mile = 100 miles per hour.
For the record, 880 feet is just under 300 yards, which means that you would cross almost three football fields in six seconds.
If you want to be as fast as possible without using step of the wind or haste, be an aarakocra monk with quintuple mobile. Without using haste or step of the wind, so just normal movement + dash action, such a character could maintain 29.55 mph indefinitely.
As far as I know this is the fastest you can go in D&D without teleporting.

(via fir-trees-unite-deactivated2017)