Speedster

Wizards who improve their speed by magic and learn how to deal damage while moving.

Level 3: Speed savant

The time and money you need to copy spells with the movement tag to your spellbook is quartered. In addition, whenever you gain a wizard level and whenever you choose this subclass, learn one additional wizard spell with the movement tag.

Level 3: Speedstrider

You always have the spell longstrider prepared, in addition, when you cast that spell, you gain the following benefits:

• Your speed increases by additional 10 ft., this feature increases to 15 ft. in level 6, to 25 ft. in level 10 and to 40 ft. in level 14.
• Your movement doesn't provoke opportunity attacks.
• You can move through other creatures' space but you can't end your turn there.

Level 6: Cutthrough

Whenever you move in other creature's space this creature has to make a Dex. saving throw against your spell save DC, on fail, it take 2d6 force damage. A single creature can take that damage in a single turn a number of times equal to the number of times you used the dash action after the end of your last turn, and after you use this feature you can't cast spells of level 1 or higher until end of your turn.

At higher levels. the damage increases by 1d6 when you get yo the following levels: 10, 14 and 18.

Level 10: Fly away

Fly- If a spell you cast would give you an additional speed, it gives you double that speed instead. If a spell you cast would change your base speed to  a speed higher than your current speed, your base speed incenrease by the amount that spell increased it an additional time.

Away- Whenever a creature misses you with a melee attack, you can take a dash action as reaction then move up to your movement.

Level 14: Unstoppable

If a creature fails a saving throw of your cutthrough ability it knocked prone, a prone creature automatically fails that throw.

Your movement can't be decreased.

While your speed is 60 or higher, you can't get knocked prone, grappled, or Incapacitated, you have advantage on Dexterity saving throws and you get +2 to your AC and initiative, you get an additional +1 bonus to your AC and initiative for each 60 ft. your speed is above 60 ft.

If you moved more than 250 ft. you get an additional action or bonus action (your choice), you can't take the magic action on that action and if you take the attack action you can atack only once.