1. The problem is to understand and use the formula for displacement in uniformly accelerated motion: $$S = ut + \frac{1}{2}at^2$$ where $S$ is displacement, $u$ is initial velocity, $a$ is acceleration, and $t$ is time. 2. This formula calculates the distance traveled when an object starts with velocity $u$ and accelerates at rate $a$ over time $t$. 3. Important rules: - The term $ut$ represents the distance covered if the object moved at constant velocity $u$ for time $t$. - The term $\frac{1}{2}at^2$ accounts for the additional distance due to acceleration. 4. To use this formula, plug in the known values of $u$, $a$, and $t$ and simplify. 5. For example, if $u=5$, $a=2$, and $t=3$, then: $$S = 5 \times 3 + \frac{1}{2} \times 2 \times 3^2 = 15 + 1 \times 9 = 15 + 9 = 24$$ 6. This means the object has traveled 24 units of distance in 3 seconds under the given conditions. This formula is fundamental in kinematics for solving motion problems with constant acceleration.