When an object moves with constant acceleration, we can derive a fundamental relationship between velocity, acceleration, and time.

Start with the definition of acceleration — the rate of change of velocity:

Here, $v_i$ is the initial velocity, $v_f$ is the final velocity, and $a$ is the constant acceleration.

To solve for $v_f$, multiply both sides by $t$:

$$a \cdot t = v_f - v_i$$

Then add $v_i$ to both sides and rearrange to get:

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