 # Linear Motion: Newton's Equations of Motion

Note by , created almost 6 years ago

## This note covers the derivations of the three equations of motion. It can be used as a follow-on from the corresponding mind map "Linear Motion" or as a stand alone resource. It is aimed at a Leaving Certificate student, or someone who has an interest in Newton and his Equations of Motion. 596 1 0  Created by alex.examtime9373 almost 6 years ago
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Equation 1: v = u + at Definition of acceleration --&gt; a = (v-u)/t Multiply both sides by t --&gt; at = v-u Add u to both sides --&gt; v = u + at

Equation 2: s = ut + (1/2)at² Definition of displacement --&gt; s =  {(u + v)/2}t Use equation 1 &amp; substitute 'u + at' for v --&gt; s = {(u + u + at)/2}t Multiply out the brackets --&gt; s = (2ut + at²)/2 Divide top and bottom lines by 2 --&gt; s = ut + (1/2)at²

Equation 3: v² = u² + 2as Equation 1 --&gt; v = u + at Square both sides --&gt; v² = (u² + 2uat + a²t²) v² = u² + 2a{ut + (1/2)at²} Use equation 2 and substitute ' s ' for ' ut + (1/2)at² ' --&gt; v² = u² +2as

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