Need help in a question regarding polynomial oracle reductions
Hint: Since $S_1$ runs in polynomial time, say $O(n^a)$, every input to the oracle has polynomial length $O(n^a)$. If $S_2 \in \mathsf{P}$, say can be decided in polynomial times $O(n^b)$, then we can simulate all the oracle calls in $O(O(n^a)^b)$.