I would interpret it as calculating some function $f(v, t)$ three times, using $v = v_1$, $v = v_2$, and $v = v_3$, with $p(t)$ being used inside $f(v, t)$. In other words, I read: Calculate $f(v, t)$ in terms of $p(t)$ for $v = v_1$, $v_2$, and $v_3$, for some $f$.

But without the context of the actual calculation, it's hard to be certain, especially when the question is written in plain English like this. In formal notation, there would be no ambiguity, for instance, but in English, it could have many different interpretations.