1. We are given the equation of motion: $$s = t + \frac{1}{2} a t^2$$ where $a = 6$ and $t = -7$. 2. Substitute the given values into the equation: $$s = (-7) + \frac{1}{2} \times 6 \times (-7)^2$$ 3. Calculate $(-7)^2$: $$(-7)^2 = 49$$ 4. Substitute $49$ back into the equation: $$s = -7 + \frac{1}{2} \times 6 \times 49$$ 5. Simplify the multiplication: $$\frac{1}{2} \times 6 = 3$$ so, $$s = -7 + 3 \times 49$$ 6. Calculate $3 \times 49$: $$3 \times 49 = 147$$ 7. Add the terms: $$s = -7 + 147 = 140$$ Final answer: $$s = 140$$