![]() This is a very simple system - all we need is the value for gravitational acceleration at a particular location and all the other values follow from that. The meaning of the constants k 1 and k 2 will be explained below. In physics, an object's velocity is the time integral of acceleration:Īnd its position is the time integral of velocity: But the methods presented here show how to derive an equation that accurately profiles an object's velocity (from zero to terminal) and position with respect to time, then compares the result with published results for the same problem, some correct, some not.Īpart from detailing the calculations behind free-fall, this page is also a Sage tutorial (as are all these pages), so even if the reader has no interest in a skydiver's rapid descent to earth, the methods used to obtain the result may be worth learning. There are a number of Web resources that provide a terminal velocity number for a given object mass and shape, and there are resources that tell you how long it takes to get to terminal velocity (although some of those results are wrong). ![]() Terminal velocity calculations represent a practical use for the Calculus of differential equations, and that's the method we'll be using. This page describes a physics problem that's more difficult than it may seem at first glance, and it presents a challenge for Sage in its present form. The Sage worksheet cells in this article should function if pasted into Sage, but if this isn't the case, try downloading the entire worksheet to acquire what may have been inadvertently left out. Click here to download the Sage worksheet used in preparing this article. ![]()
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