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

The displacement $s$ of an object under uniform acceleration is represented by the area under the velocity-time graph during time t. The total area under the graph (quadrangle DOEB) can be split into:

1. Area of rectangle DOEA

Area = AE × OE = u × t, where AE = u and OE = t

2. Area of triangle DAB

Area = `"1"/"2"`$\times \text{AB}\times \text{DA}$, where DA = t and AB = at (from the acceleration formula a = `"CD"/"t"`).

$\times at\times t$

3. Total displacement

s=Area of rectangle+Area of triangle

s = u×t +`"1"/"2"`×at×t

Newton’s second equation of motion is  s = ut +`"1"/"2"`at²

Velocity-time graph