Consider the velocity-time graph of a body as shown below:
The initial velocity is u at the point A which changes from A to B at uniform rate in time t. Let v be the final velocity which is equal to BC in the graph. OC represents the time t. A perpendicular is drawn CB from point C and AD is drawn parallel to OC. BE is the perpendicular from point B to OE. The area under OABC is the distance travelled s.
Distance travelled, s = area of trapezium OABC
OA + CB = u + v
OC = t
Therefore,
v2 = u2 + 2as
