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Speed is the rate of motion, or equivalently the rate of change of distance.
Speed is a scalar quantity with dimensions length/time; the equivalent vector quantity to speed is velocity. Speed is measured in the same physical units of measurement as velocity, but does not contain the element of direction that velocity has. Speed is thus the magnitude component of velocity.
In mathematical notation, if an object traveling at constant speed moves a distance x in time t, its speed, denoted by v, is simply given by
In many situations, objects do not move at a constant speed. For example, if a car goes 120 miles in 4 hours, its average speed during that time is 30 miles per hour, but its instantaneous speed may have varied. For an object which is accelerating or decelerating, the instantaneous speed is given by
where dx is the distance it travels in a very short period of time dt. If the object travels a total distance x in time t, its average speed over that time is given by
The Trachtenberg System is a system of rapid mental calculation, somewhat similar to Vedic mathematics. It was developed by the Ukrainian engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.
The system consists of a number of readily memorized patterns that allow one to perform arithmetic computations very quickly.
The rest of this article presents some of the methods devised by Trachtenberg. These are for illustration only. To actually learn the method requires practice and a more complete treatment.
The most important algorithms are the ones for general multiplication, division and addition. In addition, the method includes some specialized methods for multiplying small numbers between 5 and 13.