From the velocity-time graph, the distance s travelled by the object in time t, moving under uniform acceleration a is given by the area enclosed within the trapezium OABC under the graph that is,

s = area of trapezium OABC

s =

Substituting, OA = u; BC = v; OC = t

s = ……(i)

Also, velocity-time relation

v = u + at

= t ……(ii)

Substituting value of t from (ii) in (i)

s = ×

v² – u² = 2as