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

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Equation of position – Time Relation (2nd equation of motion)

Area under slope = Displacement = area of OABC

Area of OABC = Area of rectangle AOCD + Area of ADB

`"S" = "OC" xx "OA" + 1/2 xx "AD" xx "BD"`

`"S" = "OC" xx "OA" + 1/2 "AD" xx("BC – CD")`

`"S" = "t" xx "u" + 1/2"t" ("v – u") "BC – CD" =" BD"`

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

`"S" = "ut" + 1/2"at"^2`

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