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Introduction
In any school Physics course, the Newtonian equations of motion are very much a ‘stock’ item. Students learn the equations and are given a variety of problems which provide practice in determining which equation(s) to use to solve any particular problem. What is perhaps a little surprising is that in general no-one applies the well-established mathematical technique of completing the square given the standard equation: ##s(t)=ut+\frac{at^2}{2}##. In this article , we will do just that and then apply the derived equations to solve some typical problems which arise.
Completing the Square
Given: ##s(t)=ut+½at^2## write as $$ s(t) = \frac{a}{2}\left(t^2 + \frac{2ut}{a}\right)= \frac{a}{2}\left[\left(t + \frac{u}{a}\right)^2-\frac{u^2}{a^2}\right]$$ In a typical projectile problem, we might define the positive direction as upwards in which case the acceleration parameter g will be negative and the equation may be written as: $$s(t)=-\frac{g}{2}\left[\left(t –...
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Answers and Replies

  • #2
Hello, in the calculation of the two proposed examples, the order of the presentation of the development of the calculation of points 2 and 3 or (b and c) are reversed, also the result of the speed is offered in meters and not in meters over seconds in the first example.
 
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  • #3
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Hello, in the calculation of the two proposed examples, the order of the presentation of the development of the calculation of points 2 and 3 or (b and c) are reversed, also the result of the speed is offered in meters and not in meters over seconds in the first example.
Thanks for the correction(s). Have amended accordingly.
 
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