Linear Motion: Newton's Equations of Motion

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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