There is no meaningful single answer to your question. It depends in part on the caliber and mass of the bullet, air temperature, wind, type of powder utilized and amount (load), shape of the bullet, and other factors such as the intended purpose of the bullet in question. Each of the forgoing answers deals with extraordinary rather than typical situations.
There are several calculators available online in which you can plug in your data to determine the velocity of a specific bullet profile. I have provided one such link for you below. The listed site also contains additional specific information surrounding the issues brought up by your question. Typically the speed of a bullet is measured in feet per second (fps) rather than miles per huor (mph). A simple mathimatical conversion can ber performed to change the units for any speed. There are several online conversion calculators that can do this for you effortlessly. I have provided the link to one such calculator for you in the sources section below.
As I stated previously, there is no meaningful average answer for all handguns. Generaly, old fashioned big caliber handguns (45 Colt, 44 S+W) shoot a heavy bullet without a lot of gun powder behind it. Muzzle velocities for these weapons is under 1000 feet per second. Some as low as 800 feet per second or even lower.
On the other hand, some lighter caliber handguns (.223, 22-250) used for hunting or long distance target shooting use a much lighter weight bullet and have a much larger brass case behind the bullet filled to the brim with high power gun powder.
Muzzle velocities for these weapons can easily exceed 3000 feet per second. Some custom hand loaded cartridges in some light calibers approach or even exceed 4000 feet per second, but these are not typically available over-the-counter.
Using a kinematics formula, it is possible to determine the acceleration of a bullet when the muzzle velocity and barrel length of a gun are known.
v2 = vo2 + 2as
where:
v is the muzzle velocity
vo is the initial velocity of the bullet, which is zero
a is the acceleration
s is the barrel length
Since acceleration is the desired value in your question, the derived formula is this:
a=v^2/2s
When fired from a Beretta 92S, the standard issue US Army pistol, a 9 mm Parabellum bullet has a muzzle velocity of 335 m/s. With its 127 mm barrel length, the bullet's acceleration is calculated to be 4.4 × 105 m/s2.
The acceleration of a bullet depends largely on the gun from which it is fired, along with the intent of the user. Pistol bullets generally feature a lower acceleration than rifles or machine guns. Also, individuals involved with clandestine operations may use firearms with silencers, which suppress bullet speed and require special subsonic ammunition.
The "aught-six" fires a 180-grain bullet (one grain weighs one seven-thousandth of a pound) with a velocity of about 2,700 fps, a combination producing about 2,900 foot-pounds of energy.
Examining the less than typical, tanks employ much larger tungsten-carbide projectiles driven at velocities in excess of 4,000 feet per second. At that velocity, the big projectiles literally melt their way through all but the newest, toughest armor.
Getting still more velocity is not easy. Chemical propellants cannot push a bullet beyond the speed at which the detonation wave propagates through the explosive and into the surrounding gases. Worse, though there are high-speed explosives such as Primacord or some plastiques with detonation velocities above 20,000 fps, there are physical barriers to driving explosively propelled projectile that set in at around 6,000 fps. You can stuff in all the propellant you want, and you'll not exceed that velocity a whit.
The military designers have set out to circumvent the limitations imposed by chemical propellants. In effect, they've traded a bang for a zap: they've come up with the Electromagnetic Gun (EMG).
EMGs work like linear electric motors. Like an ordinary rifle, an EMG has a breech, barrel, and muzzle. Its bore is different; it has two parallel copper rails, one on each side. With a projectile at the breech between the rails, an electric current is applied. The current forms a magnetic field behind the bullet. As current flows between the rails, the moving magnetic field accelerates the bullet down the whole length of the barrel.
Using this technique, three independent laboratories have produced velocities beyond 26,000 fps. If somehow a 180-grain .30/06. bullet could be kept from disintegrating instantly when propelled at that velocity, it would achieve 270,000 foot-pounds of kinetic energy at the muzzle-equivalent to a ten-ton eighteen-wheeler traveling at 20 miles per hour.
Spending a brief moment on this line of thought, of course, something as light as a standard rifle bullet would merely splash on hitting a plate of tank armor. The military's problem is to send a heavy projectile at hypervelocities. They seem to be well underway toward doing just that: the Army and its contracting agencies recently tested a 90-millimeter EMG called "Miramar Gun B" that successfully shot a projectile weighing more than two pounds at a velocity of 11,154 feet per second. That yields a stupefying 4,300,000 foot-pounds of energy---the equivalent of that ten-ton semi traveling at 80 miles per hour.
Good luck and feel free to contact me if the need should arise.