Mechanics (Paperback)

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER II MOTION VIII.?How Velocity is Defined. As we shall see, motion holds a very important place in Mechanics; its nature must be perfectly understood, and we had better study it first alone. We shall thereby be diverted for a short time from the principal object of our study, but it will thereby be all the easier and will yield better results. Though we may lose a little time now, we shall gain much later on. At first sight no difficulty is apparent in defining motion completely. Given the speed and direction of a moving body, we know where it has come from, where it is going, and in what time it will travel a certain distance. Its speed can, it is true, be given in miles per hour, in feet per second, in kilometres per hour, in metres per second, or in any other units; the transition from one system to another is simply a question of arithmetic, and will not detain us for a moment. Yet, when we are told a train travels 60 miles an hour, are we sure that we fully understand ? Not if this is the only information, for it can have many separate meanings for a traveller. We can say, for instance, that the journey from New York to Albany is done at 60 miles per hour, or that the express from New York passing through Y nkers at a speed of 60 miles per hour collided with a freight train. In one case we mean that the total number of miles between New York and Albany, divided by the number of hours of the journey, gives 60 as the result; in the other case, that if thetrain had continued at a uniform speed, it would have gone 60 miles in an hour. The first calculation gives what may be called commercial velocity; this is composed of a combination of all the speeds from stoppage to the maximum speed on the straight parts of the track. If there had been no stopp...