1. The problem is to express the velocity $v$ in terms of initial velocity $v_i$, acceleration $a$, and time $t$ in standard kinematics. 2. The standard formula for velocity under constant acceleration is: $$v = v_i + at$$ This formula states that the final velocity $v$ is equal to the initial velocity $v_i$ plus the product of acceleration $a$ and time $t$. 3. Important rules: - Acceleration $a$ is assumed constant. - Time $t$ is the elapsed time. - Initial velocity $v_i$ is the velocity at time $t=0$. 4. There is no further simplification needed as the formula is already in its simplest form. 5. Therefore, the velocity at time $t$ is: $$v = v_i + at$$ This formula can be used to calculate the velocity of an object moving with constant acceleration after time $t$.