2.5 feet per second per move action.
Mage Hand says:
As a move action, you can propel the object as far as 15 feet in any direction
Which means that the object can move as long as you have enough Move Actions to move it. Regardless of how fast you think that move action is, it cannot be longer than the 6 seconds that is the duration of a Combat Round.
So, the more move actions you use, the "faster" the object moves:
- You have a Move Action every round.
- You can downgrade a Standard Action to a Move Action.
- You can use a Hero Point to obtain either a Standard Action or
a Move Action.
- You can use use the Pathfinder's Chonicler's Inspire Action to
obtain another Move Action.
- And any other ability that could grant your extra Move (or Standard) Actions.
With 2 move actions, the object moves 30 feet, or 5 feet per second (about 1.524 m/s).
With 3 move actions, the object moves 45 feet, or 7.5 feet per second (about 2.286 m/s).
With 4 move actions, the object moves 60 feet, or 10 feet per second (about 3.048 m/s).
And so on, increasing the speed by roughly 2.5 feet per second (or 0.762 m/s) per Move Action used to move the object.
P.S: No, it's not fast enough to hurt someone. That's what Telekinesis and Telekinetic Projectile are for. If the spell could cause damage, it would say so in its description.
Ideally, Sacred Flame kills it (roughly) twice as fast
A simple formula answers this, with X being the number of rounds needed to kill the Shadow.
1d10 averages 5.5, halved is 2.75
1d8 averages 4.5, doubled is 9
For Firebolt, you hit on 8-20 (chance for crit), so .65 x (5.5/2)(crit bonus)x(XFB) >= 16
(Need to hit AC 12; roll 1d20 +2 Int +2 proficiency)
(14 / 13 = crit factor; (x+1)/x for damage with the chance of crit thrown in)
For Sacred Flame, you hit on 13-20 (and no crit) .4 x (4.5 x 2)(XSF) >= 16
With a DC of 11 (you only have +1 due to your 12 Wisdom)
(The Shadow makes a dex saving throw versus the spell)
Solve for XFB: 16/(.65 x 2.75 x 1.077) = 8.31 rounds
Solve for XSF: 16/(.4 x 9) = 4.44 rounds
As a practical matter, being able to kill it in ~4 rounds rather than ~8 rounds means that your Sorcerer with that meager 16 HP has a far better chance to survive the fight before having no offensive capability.
Actions
Strength Drain. Melee Weapon Attack: +4 to hit, reach 5 ft., one creature.
Hit: 9 (2d6 + 2) necrotic damage.
Two hits and your Sorcerer is down.
This is an encounter were the Cleric's "turn undead" would be a handy skill to have.
This whole problem also presumes that you stay more than five feet away from the Shadow. In the case of firebolt, since that is a ranged spell attack rather than a spell that calls for a save, if the Shadow closes to melee range your firebolt attacks at disadvantage.
(SRD p. 103; spell attacks) Most spells that require attack rolls involve ranged attacks. Remember that you have disadvantage on a ranged attack roll if you are within 5 feet of a hostile creature that can see you and that isn’t incapacitated.
Best Answer
A typical caster can't use mage hand to make attacks
The 0-level Sor/Wiz spell mage hand [trans] (Player's Handbook 249 and also for Pathfinder here) has the entry Duration: Concentration. So, after the caster takes a standard action to cast the spell, each turn the caster must take a standard action to maintain the spell, and that leaves the typical caster without the standard action necessary to make attacks with whatever the mage hand spell effect is toting: the caster essentially spends his standard action solely to move around the affected object (just as the spell indicates) rather than spending his standard action to use the affected object violently like he could naturally with an effect like, for example, the spell telekinesis.
Thus, in the same way a typical creature can't take a move action to make an attack, a caster can't just move an item that's affected by the mage hand spell so that the affected object makes an attack. Like this fine answer suggests, dropping an affected object on a foe and using an object to trigger a trap are likely the best ways for a typical caster to use the mage hand spell in combat.
"But what if he can?"
This DM would rule that a caster that employs the spell mage hand to affect a less-than-5-lb. mundane weapon, keeps that weapon within the mage hand spell's close range, and somehow acquires on his turn a second standard action (or somehow manages to concentrate on a spell using an action other than the caster's standard action) could, in fact, make with that weapon one attack… or, if the caster's actions allowed, even make multiple attacks with that weapon.
In such a case, this DM would have the caster make the attack roll using the caster's base attack bonus and, instead of the caster's Strength or Dexterity modifier, the mage hand spell's caster's spellcasting key ability (much like the using the violent thrust version of the aforementioned telekinesis spell). However, the mage hand spell can only carry 5 lbs., and, according to carrying capacity, that puts its Strength score between 1 and 2. Because of this, this DM would rule a weapon the mage hand spell effect employs suffers a −4 penalty on damage rolls.
Further, as the weapon isn't being wielded by a creature, the weapon doesn't threaten an area, therefore it can't, for example, help an ally flank a foe or make attacks of opportunity. (This DM would likely look to the spell spiritual weapon for guidance, that spell also seeing a weapon attacking on its own accord at a distance yet at the caster's behest.)
Seriously, though, in this case, this reader believes that a caster who has available on his turn two or more standard actions should be able to find something better to do with those standard actions than to use the first to concentrate on the mage hand spell and the second to make an attack with whatever that mage hand effect's carrying! I mean, c'mon: You're a wizard with two standard actions per turn: Stop toying with your foes and end this already!