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The cannon (also called artillery or gun or field piece) has no acceleration. It's just a stationary tube; a gun barrel.

The cannon ball (also called a shell or projectile) travels at a speed determined by it's propellent charge; interior of the gun tube (rifled or smoothbore); length of gun tube; and the caliber of the weapon (gun size).

As a rule: Larger projectiles travel slower; rifled barrels shoot slower projectiles; shorter gun tube have shorter ranges; smaller powder charges (propellent) travel smaller distances.

I'm sorry, but the cannon does accelerate in the opposite direction of the cannon ball. This is called recoil. Old cannons simply rolled backwards as a result of recoil and had to be manually pulled forward again and reaimed. Modern artillery pieces all use recoil absorbing mechanisms that permit the barrel to recoil without moving the carriage, then automatically reextend the barrel.

To answer the original question, the cannon is heavier and the ball is lighter, therefor the ball accelerates faster than the cannon.

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Q: Why does a cannon and a cannon ball have different accelerations when it is fired?
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Related questions

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