A) Set and solve for
B) The acceleration is Substitute the values of you found in (A) into this. The accleration is positive if its speed is increasing.
C) The displacement is Substitute to find the constant of integration.
D) If you sketch the curve of against , you should find that the minimum displacement of the object is at
PS: I rather think they want you to find the leftmost position of the object for (not 0). In this case, use the results you found in (A) and (B) to find the minimum value of for (it would be at the time when the velocity is zero and the acceleration is positive).