Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 1, Problem 29AP
To determine

To determine: The distance differs from 100m and from 1000m by equal factors.

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In a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 m = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We could equally well write 6.375 m = 6.37 m, “rounding down” instead of “rounding up,” because we would change the number 6.375 by equal increments in both cases. Now consider an order-of-magnitude estimate, in which factors of change rather than increments are important. We write 500 m ~ 103 m because 500 differs from 100 by a factor of 5 while it differs from 1 000 by only a factor of 2. We write 437 m ~ 103 m and 305 m ~ 102 m. What distance differs from 100 m and from 1 000 m by equal factors so that we could equally well choose to represent its order of magnitude as ~ 102 m or as ~ 103 m?
A useful and easy-to-remember approximate value for the number of seconds in a year is A x 10's. Determine the percent error in this approximate value given that there are 365.24 days in a year (the 0.24 days are why we have leap days every four years).
Suppose quantity s is a length and quantity t is a time. Suppose the quantities v and a are defined by v = ds/dt and a = dv/dt. (a) What is the dimension of v? (b) What is the dimension of the quantity a? What are the dimensions of (c) ∫vdt,∫vdt, (d) ∫adt,∫adt, and (e) da/dt?   Thank you for your help and time, I think I got this but I am a little confused.

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