Is it possible to calculate an acceleration for a body which starts from rest and achieves a certain speed in the given time frame?
Yes
Yes, it is possible to find the acceleration 'a'. We need to use the first equation of motion i.e.
v = u + at
Since, the object starts from rest u = 0, t is known and v is also known. So one can easily find acceleration 'a' in this case.
We get, v = 0 + at
or v = at
i.e. a = vt