Mathematician's Delight by W. W. Sawyer

Author:W. W. Sawyer
Language: eng
Format: epub
ISBN: 9780486137001
Publisher: Dover Publications
Published: 2012-10-14T16:00:00+00:00

TABLE VIII

Just the same argument can now be applied again. In the tenth of a second between 0·9 and 1 the stone covers 0·19 of a foot. This represents an average speed of feet a second - that is, 1 ·9 feet a second. In the same way, the average speed in the tenth of a second just after 1 second is 2·1 feet a second. The number we want therefore lies between 1 ·9 and 2·1. In getting this result, we have not had to carry out any process more complicated than ordinary division.

But there is no limit to the accuracy we can obtain by this method. If we consider the hundredth of a second just before, and the hundredth just after, 1 second, we find that the speed lies between 1 ·99 and 2 ·01 feet a second. If we take a thousandth of a second, we find the speed lies between 1 ·999 and 2·001. And there is nothing to stop us considering a millionth or a billionth of a second if we want to. Only one speed will satisfy all these conditions - exactly 2 feet a second. And that is the answer to our question.

In exactly the same way you find the speed after 2 seconds. The little table may then be read:

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