Question

if a particle starting with certain initial velocity and uniform accelration covers a distance 12m in first 3 seconds and a distance of 30m in next 3 seconds.then find its inital velocity

Answer 1

(vi+v3)/2 = 12/3 = 4 and (v3+v6)/2 = 30/3=10
so
v3 =8-vi and v3 = 20-v6
and
v6=vi+6a
so
8-vi = 20 -vi -6a
or
6a = 12
a = 2
then
vi + 3(2) = v3 and vi+v3 = 8
so
vi+6 = 8-vi
2 vi = 2
vi = 1

Answer 2

I am not so sure about the answer but I think :
D1=12m ,T1=3secs ,D2=30m ,T2=3secs

Initial velocity =
V=d1/t1=12m/3secs=4m/s

Please bear with me for I just showed my opinion, any mistake can be corrected .Thanks