Notes
Linear Motion: Newton's Equations of Motion
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Equation 1: v = u + at
Definition of acceleration --> a = (v-u)/t
Multiply both sides by t --> at = v-u
Add u to both sides --> v = u + at
Equation 2: s = ut + (1/2)at²
Definition of displacement --> s = {(u + v)/2}t
Use equation 1 & substitute 'u + at' for v --> s = {(u + u + at)/2}t
Multiply out the brackets --> s = (2ut + at²)/2
Divide top and bottom lines by 2 --> s = ut + (1/2)at²
Equation 3: v² = u² + 2as
Equation 1 --> v = u + at
Square both sides --> v² = (u² + 2uat + a²t²)
v² = u² + 2a{ut + (1/2)at²}
Use equation 2 and substitute ' s ' for ' ut + (1/2)at² ' --> v² = u² +2as
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- 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.
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