Q. 204.4( 10 Votes )

Derive equation for position - velocity relation graphically.

Answer :


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


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