When you interact with an object, kicking away a dropped or disarmed weapon should be an obvious choice, landing somewhere between 'pick up a dropped axe' and 'kick a small stone,' however, there are no rules indicating how far one can kick an object. This can be fairly important. The difference between kicking a sword five feet and fifteen feet away is very significant. How is the distance any item can be kicked adjudicated?
Effectiveness of such an action should be resolved by an Ability Check.
While you are right that kicking a small object is a Free Action in combat, that doesn't mean you always succeed automatically. Sure, simple, trained actions like drawing a sword are not rolled for, but if you want to achieve a specific advantage with such action, you have plenty of interesting skills to choose from.
Most obvious would be to use a Strength check (Athletics) or Dexterity check (Acrobatics?), depending on your players description of the action. You could then place appropriate modifiers reflecting the terrain (mud, wooden floor, grass?), difficulty (Sword of Spiky Mistakes or Club of Harmlessness?) and other factors. Then, depending on whether the outcome is high medium or low you can adjudicate an appropriate distance.
Don't overthink this
Of course, the rules say little about such situations, but how many times do you imagine your players will kick something in combat? Stick to well-known simple systems and invent house-rules only if they don't work. It's more important to give a quick ruling and move on rather than ponder on what would be an accurate simulation. Treat it like a "miscellaneous" situation it is and go forth with the adventure. If your players complain, talk about the matter between sessions and decide on some rules that work for everyone.
Other than the interaction of "kicking a small stone" in the free interactions section, the system is fairly quiet about the distances of kicking objects.
In keeping with the simplicity mandate of the rules, a good rule of thumb would be half the throwing distance of a thrown similar object, which is usually 20/60. So if someone wanted to kick away a weapon, 10 feet would be a reasonable distance for a heavy weapon, and 30 feet for a light one. You could halve the distance again for difficult terrain. In no case should the kicking distance exceed the throwing distance for a similar object, unless the object is designed to be kicked (such as a football).
This really falls into the realm of a DM call, though, since the rulebook does not dwell on too many fringe cases.
This situation is not covered explicitly by the rules, but comes up quite often in one of the games I run due to a fighter with the Disarming Strike maneuver. I use a "degrees of success" roll using Strength (athletics). See the DMG for a description of this type of roll.
I set the DC as 5 + distance kicked. Since things like reach are measured in 5 ft increments and I often play using a grid, I also use increments of 5 on the distances, so the distance kicked is rounded down.
This results in a DC of 10 to kick a weapon out of an opponent's square into an adjacent one, or if not using a grid, out from under the opponent's feet, but still within reach, assuming a typical, medium sized creature. Rolling 15 or higher would result in the weapon being out of the opponent's reach or two squares. A roll of 25 would move it 20 ft or 4 squares.
In the end, a roll of at least 15 is needed to require the opponent to do more than just reach out and pick up their weapon using their object interaction, forcing them to choose between risking an opportunity attack or continuing to fight without that weapon. At low levels, this allows a PC with proficiency in athletics to successfully hamper their opponent about 1/2 the time, with the success rate rising as they gain levels. This makes disarming strike on par with other maneuvers.
For those without proficiency or high strength, the success rate is going to be closer to 1/4. However, kicking the weapon 5 feet does allow an ally to pick up the weapon from 10 ft away from the opponent, which said non-proficient PC should be able to successfully complete about 1/2 of the time.
At my table, this method has been a success. It is very simple, easy to remember, and allows the player to succeed often enough to want to attempt this, while failing often enough that they feel tension when they roll.
There's too many variables to make a simple rule. A long sword will move much further on the polished marble floor of the throne room that it will when kicked with the same force in a muddy forest clearing.
So it falls under rule 0 - the DM makes the rules.
Use the rules for throwing an object. The goal is the same (using a limb to cause an object to traverse a distance), there is no reason for the mechanic to be different.
This is a complex situation and the results would depend on
- the weapon itself: weight and configuration. Think flail versus club
- terrain: grass, mud, stone
- orientation of the weapon: sword pointing right at you versus 90° and anything in between (random chance)
- the battle: is the opponent focused on you or are others fighting it/him/her? Certainly might open the character to a free hit when he/she decides to play kick ball in the middle of a battle.
If you really wanted to explore this, I would probably make up a table with weapon types versus distance with modifications for items 2 and 3 (and 4 if you're rushing).
Thinking this through, let's say,
Final Distance = distance from table divided by four sided die roll (rolled by player) times orientation (0 to 90° rolled by GM)/90 * terrain factor
No, I have not tested this system as I've never had a player try to kick a weapon.