v = at1
i.e. t1 = v/a
0 = v - bt2
i.e. t2 = v/b
So, total time of travel is t1+ t2 = v(1/a +1/b)
Now,
v2 = 2as1 or s1 = v2/2a
0 = v2 - 2bs2 or s2 = v2/2b
So, total distance = s1 + s2 = v2/2 . (1/a + 1/b)
So, avg. speed = total distance / total time
= v/2