1. The problem is to understand and use the equation for displacement in uniformly accelerated motion: $$\Delta y = v_i \Delta t + \frac{1}{2} a \Delta t^2$$ 2. This formula calculates the change in position ($\Delta y$) of an object moving with initial velocity $v_i$, acceleration $a$, over a time interval $\Delta t$. 3. Important rules: - $v_i$ is the initial velocity. - $a$ is the constant acceleration. - $\Delta t$ is the time elapsed. - The term $\frac{1}{2} a \Delta t^2$ accounts for the displacement due to acceleration. 4. To use this formula, plug in the known values for $v_i$, $a$, and $\Delta t$, then calculate each term step-by-step. 5. For example, if $v_i=5$, $a=2$, and $\Delta t=3$, then: $$\Delta y = 5 \times 3 + \frac{1}{2} \times 2 \times 3^2 = 15 + 1 \times 9 = 15 + 9 = 24$$ 6. This means the object moves 24 units in the time interval $\Delta t=3$. This formula is fundamental in kinematics for calculating displacement under constant acceleration.