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Continue reading...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 –...