While some of nature's limits like the speed of light, are probably impossible to break, humanity has been breaking the sound barrier since before recorded history.
Remarkably, whenever someone cracks a whip, they actually make the tip of the whip move faster than the speed of sound. The crack that you hear is actually a miniature sonic boom.
How can this be? No one can move their arm faster than the speed of sound, so how can you make the tip of a whip move that quickly? The answer can be found in the physics of wave motion.
When you begin to crack a whip, you move your arm sharply up, then down. This causes a wave, like an upside-down letter U, that begins traveling down the length of the whip. The total energy of this wave is determined by the mass that is moving, or in this case the thick, ropey mass of the whip, and the speed that the rope is moving.
When the wave begins, it's only moving as fast as your arm can move, which is nowhere near the speed of sound. As the wave moves along, however, the whip begins to taper. It starts out thick and ropey, but it narrows to just a thin wisp. This means that as the wave progresses, it has smaller amounts of mass to move up and down. Since the total energy is determined by mass and speed, as the mass decreases, the speed of the wave needs to increase. By the time it reaches the tip, the wave has enough speed to break the sound barrier, and snap out a lively sonic boom.