ACCELERATION

(Lat. acceleratio, hastening.) In Mechanics, an increase in the velocity of bodies in motion. Acceleration is uniform or variable, according as the force by which the motion is produced acts regularly or irregularly. The most familiar instances of uniformly accelerated motion, are those which are occasioned by the earth's attraction, and are exhibited in the falling of heavy bodies, or their descent along inclined planes. In both these instances, the observer cannot fail to perceive that the velocity becomes greater as the body falls from a greater height, or continues a longer time in motion. In order to explain the theory of acceleration from the action of gravity, it is nece ary to recollect that, in virtue of the inertia of matter, a body always perseveres in its state of rest, or of uniform motion in a straight line, till, by some external influence, it is made to change its state. This is Newton's first law of motion, which is admitted as a principle or axiom in mechanics, and from which it follows, that as a body cannot accelerate its own motion, any change iij the rate of velocity of a moving body must arise from the action of an extraneous force. Now, suppose a body to be carried to a considerable height above the earth, and abandoned to the action of gravity; and let us examine the circumstances which take place. In this supposition, gravity may be regarded as a force acting uniformly; for, though its intensity diminishes as the distance from the centre of the earth increases, yet any height to which we can reach is so small, compared with the radius of the earth, that the variation in the intensity of gravity depending on it may be disregarded. Let the time which the body takes to fall to the earth be divided into equal and small intervals. During the first interval an impulse is given to the body, and a certain motion is communicated. If gravity now ceased to act, the body would continue to descend uniformly with the velocity it had acquired; but the impulse is renewed with exactly equal vigour during the second interval, and, consequently, the velocity of the body is exactly-doubled. The same thing is repeated in the third interval, and, consequently, the velocity of the body is then tripled. In the fourth interval it is quadrupled, and so on; the body continually receiving, during equal and.succe ive intervals of time, equal increments of velocity from the action of the accelerating force, and preserving its acquired velocity in consequence of its inertia. Hence we infer the first great law of uniformly accelerated motion, namely, the velocity at any given moment is proportional to the number of impulses that have been received, or to the number of intervals that have elapsed since the commencement of the motion; in other words, the velocity is proportional to the time. Let us now consider the spaces pa ed over by the falling body. Suppose the space through which the body falls during the first interval, or second of time, to be one pole. As the velocity is supposed, at the commencement of the motion, to be nothing, and to increase uniformly during the interval, it is evident that the space pa ed over will be the same as if the body had continued during the interval to move uniformly with the mean velocity, or the velocity it had at the middle of the interval. But the velocity has been shown to be projjortional to the time. Hence, at the end of the first second the velocity is the double of what it was at the middle of the second; and, therefore, if gravity ceased to act, the body, during the second interval or second, would descend through two poles. In consequence, however, of the renewed action of gravity, the body receives a fresh impulse during the second interval equal to that which it received during the first, and is, consequently, carried through a space equal to one pole, in addition to that B4 [s. 20]