Why would one not be able to accelerate a 1 pound object to lethal velocity with a mage hand?  By my calculations, 1 pound of the hand force would be holding up my 1 pound object, allowing 9lbs of force to act on the object or 9 x gravity.  Over 30', this would result in an 1 pound object moving roughly 94 MPH.  Or the energy in a 9mm bullet. And that assumes a straight line, one could spin the object around, until it reach max centripetal force (9x gravity), that would add an addition energy making the 1 pound object hit at 210 MPH or just under a 12 gauge shot gun round of energy.  

Can you provide the equation for this? I'll need a way to justify this to my DM.

Short answer "for game balance, thats too powerful for a cantrip".

Long answer, I kind of agree with you though allowing a mage hand to hit someone with as much damage as a 9mm round is obviously game breaking, if you can throw 'create fire' for 1d6 fire damage mage hand should at least be able to do the same with a thrown object and should at least be able to attempt to punch for unarmed damage...

it's a spectral hand. It can't punch.

The hand has a carrying speed that is the same. You will carry the 1 pound item and a 10 pound item with the same speed. This is not a directional force so it cannot provide velocity. You need the Catapult spell if you want to do such thing.

Meh. If a 'spectral hand' can exert force on a physical object it can exert force on any physical object. There's no logical reason it can pick up a 10 lb sack but can't push someone with the same 10 lbs of exerted force.
Based on RAW, it can only move 30 ft over a period of 6 seconds (or about 3.5 MPH) which is definitely not a punch level strength. This is a more logical reason the spell wouldn't work for damage in that way. 

30' in 6 seconds is 3.4 mph, not 94, 6 seconds is 1/10th a minute, 1/600th an hour, 30' x 600 = 18000, 18000/5280 = 3.4 MPH

The math I used was 1 pound object moving 30' at 9Gs, so takes .456 seconds to get there, going 131 ft/sec or 89MPH.    Given a wall of force, one could get it to go a lot fast before wind resistance over comes 9Gs of force, but based on my calculation, a lot of energy of impact (like 150 shotguns, if I remember correctly).  Given a full round (6 sec), it would have a speed of 1728 ft/sec or 1078 MPH, so again a lot of energy (circular wall of force required to contain).  

G = 32 ft/sec^2

Distance = V init*time + 1/2A*time^2  

Speed = V init + A *time 

On the punch thing, I kind of agree that it wouldn't have mass and thus no energy.  But it raises an interesting though, if you pushed 10 lbs into something the size of a dagger or pin, it would be more than enough force to do damage.  Or referencing one of my favorite book series, just kill with a spear of force to the heart or brain. Magic is cool.

Ottaviani's right.  It's magic.  The hand can't impart velocity or momentum: magic doesn't follow physics, that's what makes it magic.  Magic does what it does, it isn't flexible.  The mage hand spell moves things slowly, catapult is for moving them fast enough to hurt.

Can this spell work as a conduit for touch spells like shocking grasp & vampiric touch?  Or is that strictly done through the wizard's familiar now?

The touch spells can be delivered by a familiar, but they cannot be delivered via Mage Hand.

One of many changes from 2E.  Thanks :)

I want to point out GMO is right in that the rules as written totally allow for the hand to perform this action, and the calculations check out. To quote the rules as written, "you can use the hand to manipulate an object," and "you can move the hand up to 30 feet each time you use it." The text places a limitation on the distance moved in one action, and not on the speed of that movement. I imagine it can make lightning-fast movements, as long as it's not across a distance of more than 30 feet in that action.

However, (and this is the cinch,) the spell also states that the hand can't attack. Whatever movements the hand takes, be it a punch or accelerating a rock to lethal speeds, it can't be treated as an attack. It's up to the DM whether they'd consider this simply moving an object or an attempted attack... Personally, I think it's obviously an attack. Indirect actions such as loosing a chandelier or nudging a boulder off a cliff wouldn't be considered as such and would end up dealing damage.

If one of my players brought this up and tried to do it, I would allow the given motions, but it would deal no damage. I'd ask them to make an Intelligence (Arcana) check every time they attempt Mage Hand this way, with something like the following results:

• Roll of 1-11 (Anything below average for an adventurer)
• You just don't get why it's not working.
  
• DC-12 (10 + Proficiency Bonus of any 1st-level adventurer) Returns basic knowledge of the cantrip.
• Mage Hand is a cantrip-spell primarily for moving things, not killing people.
• DC-15 (10 + Proficiency + Intelligence of any clever 1st-level wizard) Returns some creative uses of what they're trying.
• You might be able to launch something with a written note on it this way, or even hit a button or ring a bell from a distance. This cantrip still doesn't seem to be doing damage, though.
• DC-19 or 20 (14 or 15 + Proficiency + Intelligence) Returns exactly what they need to do for this to work.
• You may have to expend considerable focus and mental effort to deal lethal damage next time.
• First roll only: Scholars studying the applications of Mage Hand found they'd have to expend considerable focus and mental effort to make this situation work out to deal lethal damage.

 Once they figure out that they can expend a spell slot, they may pick up heavier objects (up to 5 lbs) and use the spell to deal 3d8 bludgeoning at a range of 60 ft, increasing by 1d8 for each spell slot above 1st. At the end of the session, I'd allow them to add the Catapult spell into their spellbook.

(Mage Hand calculations are contained in the following spoiler, if anyone's interested. It assumes the 10-lb carry weight means it can't impart more than 10 lbs on anything.)

Concerning the possibility of using the magic hand as an offensive mean (beside showing the magical middle finger to someone :P): you guys are misinterpreting the description or are forcing a concept based on "what's not explicitly written".

While it's true that it doesn't clearly states the speed of movement, it's pretty obvious that "up to" means that this is the maximum distance covered in 6 seconds; said that, it would be silly being able to get there in just one second, spending the remaining 5 wondering why you can't push it any further. It's not a matter of joules, but a mere question of speed. Believing otherwise it's just wishful thinking.

Ad such speed, even provided that you can move the magic hand directly from 0 to max speed instantaneously, there isn't enough force to deal any damage with a thrown object.

What's questionable, is that with a tiny pressure point, say a stiletto, I could actually penetrate and stab someone's stomach with the weapon. Why can't I use the hand like that?

Spellword is: Handicus Toolium

Not sure how nobody has brought this up yet, but can you throw a 1 pound object 94 miles per hour?

im sure that you can also lift a 10 pound object, like curling a dumbbell, but that doesn’t mean you could accelerate that object indefinitely over time. You can exert the necessary force with your hand to lift and manipulate objects, but applying substantial force over the course of any time period is another matter altogether.

we could do the math together on acceleration rates of a baseball (which I believe weighs 5.5 oz) but the simple answer is you know it won’t work. 

I imagine that a 30 foot movement speed insinuates the hand accelerates to 5f/s pretty quick, but that is its top speed. So regardless of how much force is required to accelerate the object that quickly, that fastest it can accelerate any object to is 5f/s, which is relatively harmless. 

Could the hand hold a sheild

A shield weighs six pounds. So, yes! Some might say the spectral hand would then have +2 to its AC. I’m not sure how useful that would be. I wouldn’t consider that as being wielded but I might give them something if they tried using it as a held action. Though taking the Dodge action would probably be better. In fact I think that’s exactly how I’d handle it. What a cool special effect for a Dodge!

Regardless, it would also make a mighty fine umbrella.

I personally use flintlock pistols in my campaign.  Would it be possible, if sed pistole was 3lbs, to make the mage hand preform the simple task of picking up the pistol and pulling the trigger? 

People keep talking about using this hand for things like firing guns or leaning a weapon in. The hand can't make attacks. Pulling the trigger on a weapon or pushing a blade into a person is an Attack. Throwing something at a person with intent to hit and damage is an Attack. Pushing a blade into someone is stabbing, and is an Attack.