Growth Functions

  • Arthur L. Loeb
Part of the Design Science Collection book series (DSC)

Abstract

If you drop a ball from a given height, its velocity will increase at a constant rate called the acceleration of gravity:
$$\frac{{dv}}{{dt}} = g.$$
(17-1)
Integrating, we find that v = gt, assuming that at time t = 0, the moment at which the ball was dropped, the ball had zero velocity. Actually the velocity is itself the rate at which the altitude of the ball decreases:
$$v = - \frac{{dh}}{{dt}}$$
Since \(v = gt,\tfrac{{dh}}{{dt}} = - gt\), and \(h = {{h}_{0}} - \tfrac{1}{2}g{{t}^{2}}\) where h 0 is the initial height from which the ball was dropped at time t = 0.

Keywords

Europe Catalysis Metaphor 

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Notes

  1. 2.
    Loeb, A. L.: Synergy, Sigmoids and the Seventh-Year Trifurcation, The Environmentalist, 3, 181–186 (1983)Google Scholar
  2. 2a.
    Loeb, A. L.: Synergy, Sigmoids and the Seventh-Year Trifurcation, reprinted Chrestologia, XIV, #2, 4–8 (1989).MathSciNetGoogle Scholar
  3. 4.
    de Sola Price, D. J.: Measuring the Size of Science, Proc. Israel Acad. Science and Humanities, 4, 6 (1969).Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Arthur L. Loeb
    • 1
  1. 1.Department of Visual and Environmental Studies, Carpenter Center for the Visual ArtsHarvard UniversityCambridgeUSA

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