Consider the velocity-time graph of an object that moves under uniform acceleration as shown in the figure (u ≠ O).
From this graph, we can see that initial velocity of the object (at point A) is u and then it increases to v (at point B) in time t. The velocity changes at a uniform rate a. As shown in the figure, the lines BC and BE are drawn from point B on the time and the velocity axes respectively, so that the initial velocity is represented by OA, the final velocity is represented by BC and the time interval t is represented by OC. BD = BC – CD, represents the change in velocity in time interval t. If we draw AD parallel to OC, we observe that
BC = BD + DC = BD + OA
Substituting, BC with v and OA with u, we get
v = BD + u
or BD = v – u
Thus, from the given velocity-time graph, the acceleration of the object is given by
A = Change in velocity \over Time taken
= BD \over AD = BD \over OC
Substituting, OC with t, we get
a = BD \over 𝑡 or BD = at
From equations (1) and (2), we have
v – u = at or v = u + at
