You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.And from pages 190 & 191:
Standing up takes more effort; doing so costs an amount of movement equal to half your speed.So my thinking is that as a trained adventurer surely one could draw a weapon as quickly as getting up off the ground. So here is what I'm going to rule regarding drawing a weapon.
Anyone can draw one weapon as a free action as stated above. If character has already used their free action and wishes to draw a weapon that they are proficient with, they may use half their movement speed to draw that weapon. If a character has less than half of their movement remaining or the they are not proficient with the weapon they wish to draw, then they must perform the Use an Object action as normal.
You may also use your Bonus Action - should you have one - to draw any weapon.