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Equations of Motion by Graphical Method - Derivation of Position - Velocity Relation by Graphical Method

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Equation of position – Velocity Relation (3rd equation of motion)

Area under slope = Displacement = Area of OABC

`"Area of trapezium OABC" = 1/2 xx ("BC + OA") xx "OC"`

`"S" = 1/2 xx ("v + u") xx "t"`

By 1st eq of motion   v = u + at

`"S"= 1/2 xx ("v + u") xx ("v – u"/"a") ["v - u"/"a" = "t"]`

`"S" = "(v + u)" "(v – u)"/ "2a" "(a + b) (a – b)" = "a"^2 – "b"^2 `

`"2as" = "v - u"`

`"v"^2 ="u"^2- 2"as"`

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