VELOCITY, in all its significance, involves the notion of direction of motion as well as that of speed or rate of mo tion. The notion of speed is a very familiar one. In measuring it we as sume the possibility of measuring space and time; and the unit of speed is that speed which a moving point would need to have in order to pass over the chosen unit of space in a unit of time. Such phrases as four miles per hour, one mile per minute, eighteen miles per second, are perfectly intelligible to all who know what a mile, hour, minute, and second are. It should be noted that when we speak of a man walking with a speed of four miles an hour we do not necessarily imply that he really completes four miles, or that he walks for one hour, but only that he would do so were he to keep up that speed for the time named. In fact, speed is an instantaneous property of the mov ing point. Again since at every instant the moving point must be moving in a definite direction, as well as with a de finite speed, it follows that velocity also is an instantaneous property. If it does not change from instant to instant, the velocity is constant, and the point moves in a straight line with constant speed.
If the point moves in any other than a straight line, the velocity will be variable even although the speed should remain constant; and the most general change of velocity involves both change of direction and change of speed. Velocity is in fact a vector quantity, and may be treated mathematically as a VECTOR (q. v.).
The rate at which velocity changes is called acceleration. When the velocity changes in direction only, as when a point moves with constant speed in a circle, there is no acceleration in the di rection of motion—i. e., parallel to the velocity. The acceleration must there fore be wholly normal to the velocity, and will be toward the center of the circle in the simple case of uniform circular motion. If any change of speed occurs it is due to an acceleration acting paral lel to the velocity, and therefore tangen tial to the path pursued by the moving point. When only a tangential accelera tion exists, the point will move in a straight line with variable speed. A body falling vertically near the earth's sur face gives a very good illustration of a pure tangential acceleration.