1. **State the problem:** Make $a$ the subject of the second kinematic equation of motion, which is $$s = ut + \frac{1}{2}at^2$$ where $s$ is displacement, $u$ is initial velocity, $t$ is time, and $a$ is acceleration. 2. **Formula and rules:** We want to isolate $a$ on one side of the equation. This involves algebraic manipulation such as subtraction and division. 3. **Start with the equation:** $$s = ut + \frac{1}{2}at^2$$ 4. **Subtract $ut$ from both sides:** $$s - ut = \frac{1}{2}at^2$$ 5. **Multiply both sides by 2 to eliminate the fraction:** $$2(s - ut) = \cancel{2} \times \frac{1}{\cancel{2}} at^2 = at^2$$ 6. **Divide both sides by $t^2$ to isolate $a$:** $$\frac{2(s - ut)}{\cancel{t^2}} = a \cancel{t^2} / \cancel{t^2}$$ 7. **Final formula for $a$:** $$a = \frac{2(s - ut)}{t^2}$$ This means acceleration $a$ is twice the difference between displacement and initial velocity times time, divided by the square of time. This completes the solution.