Consider the velocity-time graph of an object that moves under uniform acceleration as shown in the figure (*u *โ 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 = Changeย inย velocity \over Timeย taken

= BD \over ADย ย = BD \over OC

Substituting, OC with *t*, we get

a = BD \over ๐กย or BD = *at *

From equations (1) and (2), we have

*v โ **u **= *** at**ย ย

**orย ย**

*v =*

*u + at*