For additional meanings of "Velocity", please see Velocity.
In physics, velocity was the rate of change of position along a straight line with respect to time.
Ion propulsion was a unique technology known to achieve high velocity. (TOS: "Spock's Brain")
The Tholian ship encountered by the Enterprise, near the location of the lost USS Defiant, was noted as being at a range of 200,000 kilometers at a velocity 0.51c. (TOS: "The Tholian Web")
At warp 7, the shuttlecraft Cochrane had reached critical velocity. (VOY: "Threshold")
In principle, warp 10 was believed to be defined as traveling at infinite velocity. (VOY: "Threshold")
According to Rojan, the Kelvans had achieved the know how that allowed them the ability to modify the warp engines of the USS Enterprise to give it the capability of producing velocities far beyond the reach of Federation science. (TOS: "By Any Other Name")
According to Data in 2379, Captain Jean-Luc Picard had a tendency to drive vehicles at "unsafe velocities." (Star Trek Nemesis)