Sorry if this is a duplicate, I honestly searched everywhere but didn't find this issue.
edit: this might be a duplicate of [MC-4686]
How to reproduce:
Fly very high up, let yourself fall then type:
/tp @p ~0 ~100 ~0
You'll see you start without any movement upon teleport.
I'm trying to teleport players to a same looking location, but you can still see when you are teleported because of the velocity being reset. Also your hand moves when you teleport, but that's intended (I think)
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Confirmed.

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
confirmed for 1.6.1
I don't see why this takes so long to fix. I don't know much about programming in java but can't you just add 3 temporary variables to store the velocity before someone gets teleported and then apply that to the velocity after teleportation?
Fixed in 14w02b.

This issue exists again in 1.8.1.

I can confirm it occurs in 1.8.1 and 1.8.2 pre-4. Opened a blank world, used the command while falling. It teleports me and I continue falling at the same speed, but after a few moments my character is sent back to the teleported location and velocity is reset.

Jesper, I don't even think you would need to do that. In theory location change shouldn't affect velocity. If location is stored as (x, y, z) and velocity as (Xvel, Yvel, Zvel), then changing the first set shouldn't affect the other set.
Confirmed in 15w51b.
New ticket please.
Why? It's the exact issue described here.
Reopened.

Confirmed for
15w51b
This is however not consistent for velocity caused by gravity. When you have for example a clock running /tp @p ~ ~1 ~
, the player "bounces" instead of being teleported upwards constantly (see MC-79938)
That would be MC-76463.

This is fixed in the current versions, correct?
Yes, certainly seems fixed in 16w41a.
Yes this is fixed, [MC-4686] isn't though. Not the same issue but it's related.
confirmed for 13w19a