The average acceleration of an object in motion is calculated using the formula $a=\dfrac{v_f-v_i}{t}$, where $v_i$ is the initial velocity and $v_f$ is the final velocity of an object traveling over the course of time $t$.

What is $v_i \text{ in terms of } v_f, a, \text{ and }t$?

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$$a=\frac{v_f-v_i}{t}$$ $$at=v_f-v_i$$ $$at-v_f=-v_i$$ $$-at+v_f=v_i$$ $$\boxed{v_i=v_f-at}$$