How fast is the droplet in The Three-Body Problem?
During the Doomsday Battle, the droplet attacks at roughly 3,000 kilometers per second, about one percent of the speed of light. That is the figure the books give for its strike speed as it rams the first warship in humanity's fleet.
To put that in perspective, humanity's fleet of more than two thousand stellar-class warships cruised at only tens to low hundreds of kilometers per second. The droplet's attack speed was at least an order of magnitude faster than the most advanced human ship. When it hit a warship, it passed through bow to stern like a bullet through paper, and the ship's fusion fuel detonated into a fireball. You can read the full sequence in the droplet attack breakdown.
Is 3,000 km/s the droplet's top speed?
No. 3,000 km/s is the working speed it chose for the battle, not a hard ceiling. The droplet had already crossed four light-years from the Trisolaran fleet to the Solar System, which involved far longer phases of acceleration and deceleration. Inside the human formation it needed a speed fast enough that human weapons could not react, yet controlled enough to pick off ships one by one.
What is more frightening than the droplet's speed?
Its acceleration. If the droplet were merely fast, humans could at least predict its path. What broke every defense was that it could change that speed almost instantly. When Ding Yi observed it up close, the droplet decelerated from an enormous velocity to near standstill with no sensible braking distance.
By classical mechanics, any object with mass making that velocity change over such a short distance would experience an acceleration violent enough to tear itself apart. The droplet did it without the slightest deformation. In the battle it made near right-angle turns at high speed, each turn meaning a destroyed ship. A right-angle turn at speed implies near-infinite instantaneous acceleration, which would be fatal to any known material. The droplet treated it as routine, which points to a conclusion human physicists found unbearable: it is essentially free of inertial constraints. This is the flip side of its strong-interaction material.
Why can the droplet survive its own speed?
The answer is its material. The droplet's surface is made of matter held together by the strong nuclear force, harder than ordinary matter by a factor of ten trillion, and mirror-smooth down to the atomic scale. Its internal structure is locked by the strong force and does not deform under stress. Because nothing inside it can break, it can ram ships at near-relativistic speed and turn at right angles without self-destructing. The physics behind that hardness is covered in the strong interaction article.
Why did Liu Cixin make the droplet so fast?
The speed exists to erase two centuries of human technological confidence in thirty minutes. Every metric humanity was proud of — fleet size, firepower, armor — became meaningless because the droplet was not playing by the same physics. A 3,000 km/s charge plus impossible turns does not say "the enemy is stronger." It says "the enemy is a different tier of civilization." That is the coldest layer of the dark forest worldview, and it explains why Trisolaris was willing to send just one of its ten droplets against the entire Solar System.