Question

can a body at rest posses acceleration

Answer 1

No Because we know that acceleration is change in velocity over time and at rest position the velocity of object does not change with time such it has no acceleration.
 a= v/t here v= velocity of object t= time passed a= acceleration of body
 here v=0 such that acceleration would be equal to a = 0/t= 0 which proves that when body is in rest then acceleration would be 0 as velocity would be 0.
NOTE THAT TIME CAN NEVER BE 0
-AK ;)

Answer 2

No, a body can't posses acceleration at rest.
Because,
Acceleration = Rate of change in velocity
i.e, 
Acceleration = Velocity / time
Since the body is in rest, Velocity = 0
∴ Acceleration = 0/time
                        = 0
So there won't be any acceleration when the body is at rest

-Kimmus :)