Those who study the Way of Velocity are more akin to mathematicians than traditional monks. They spend an equal amount of time studying classical mechanics as they do learning to master magical energies. The constant ebb and flow of ki can be felt in and around their bodies as if they were surrounded in a torrent of water. Way of Velocity monks combine the control of their inner energy and knowledge of kinematics to displace and redirect their bodies along these waves of ki.

Some who learn to harness this power use it to help their studies of mathematics in the hopes of understanding more about how the world moves and operates. Others use the ability to travel through the flow of ki to go forth and spread their knowledge across the world. Whatever their goal, those who follow the Way of Velocity are powerful foes who use their abilities to quickly maneuver themselves and their enemies around the battlefield.

Derivative Movement

When you choose this tradition at 3rd level, you learn how to convert your body into energy and instantly maneuver through the waves of Ki that surround your body. To others, you seem to blink out of existence for a fraction of a second as your body is displaced. 

You gain the following features:

Defensive Displacement
Whenever you use Patient Defense and the enemy misses you, you can spend your reaction to Vector Step behind the enemy and take one unarmed attack against them with all of the benefits of one Vector Step. Attacking this way does not use ki.

Vector Step
On your turn you can spend 1 ki Point to channel your body through the ki surrounding you and start a Vector Step, instantly disappearing and reappearing 10 feet in any direction in an empty space you can see. Your next melee attack this turn has +1 to its attack roll and 1d8 to it’s damage. During Vector Step you count as tiny for the purposes of passing through spaces. You can extend the effect of a Vector Step by spending additional ki.

For each additional ki point you spend, the a distance you travel increases by 5 feet. Additionally the attack roll increases by +1 and the damage increases by 1d4 on your next melee attack this turn.

Opponents do not get an attack of opportunity when you Vector Step out of their range. Your momentum carries with you when you Step. You may not use Vector Step if you cannot move due to a spell or condition.

Vector Step requires no action and may only be used on your turn. You can Vector step in between extra attacks and Flurry of Blows attacks.

Impetus Step
At 6th level when you use Vector Step, you can choose to instead spend 2 Ki Points to forgo the attack bonuses and damage and take a willing creature who is not restrained with you.

Magnitude and Direction

By 6th level, you have learned how to violently push your enemies into their surroundings. If you push a creature into another creature or object that stops their movement, they both receive 1d4 damage for every 5 feet of distance they would have been pushed.

Momentum Transfer
At 6th level whenever you hit a creature that is large or smaller with the bonus damage from Vector step, you can push them 5 feet per ki used during Vector step. It takes three times the amount of ki to push a creature that is huge 5 feet.

Extra Attack

Beginning at 11th level, you can attack three times, instead of twice, whenever you take the Attack action on your turn.

Peridynamics

By 11th level, as a bonus action, you can redirect the ephemeral energy of a creature within 10 feet of you who has been dead for less than 24 hours into your own body. When you use this ability, you may use this energy in one of two ways:

• You can choose to keep the energy, restoring 1 Ki point.
• You can use the energy to instantly recall the final 30 seconds of this creatures' life. You feel the vibrations of their fading ki and can see through the creatures eyes and can see what they saw. You hear no sound, only the vision of the creature.

Constant Velocity

By 17th level, you have learned to move across not just your own ki, but the ki of others as well. As an action, you activate Constant Velocity and convert your body into ki that moves almost instantaneously. Your speed is set to 15 feet and you can move in any direction. For every creature you pass through, you can move an additional 15 feet. Constant Velocity ends when you choose to end the attack or run out of movement granted by Constant Velocity. You cannot gain movement in any way other than passing through creatures during Constant Velocity. When Constant Velocity ends, make one melee attack that is applied to every creature you passed through; each creature takes damage if the attack would hit. 

You cannot pass through the same creature more than once and can only pass through a maximum of 6 creatures. You can move through spaces half your size or larger. Opponents do not get an attack of opportunity when you move out of their range. You may not start Constant Velocity if you cannot move due to a spell or condition. Using Vector Step during Constant Velocity will cause the attack to end, even if you have movement remaining.

The number of uses per rest increases to 2 when you reach 20th level in this class.

You regain the all uses of Constant Velocity when you finish a short or long rest.