v=v1+v2/2  since

avg. velocity=total distance/total time

==> v=v1t+1/2at²/t = v1+1/2at = 2v1+at/2 = v1+v2/2.............[where v1 and v2 are initial and final velocities]

 

but in case of  non uniform acceleration,

v=v1t1+1/2a1t1²   + v2t2+1/2a2t2²  /(t1+t2)....................[v2 is the final velocity in the first condition and initial velocity in second condition]

 

v = t1(v1+v2) + t2(v2+v3)/ 2(t1+t2)