When you shoot a bullet straight upward, doesn’t it accelerate upward?

When you shoot a bullet straight upward, doesn’t it accelerate upward?

When you shoot a bullet upward, is does accelerate as long as it’s in the gun. The burning gases push upward on the bullet and it accelerates upward. But as soon as it leaves the gun, it’s a falling object, with the only force on it being gravity (and air resistance).