Speed Bounds 6B8681

1. **State the problem:** We need to find the lower and upper bounds of speed $s$ given $d = 180$ metres (2 significant figures) and $t = 7.2$ seconds (2 significant figures) using the formula $s = \frac{d}{t}$. 2. **Understand bounds for $d$ and $t$:** - For $d = 180$ (2 s.f.), the lower bound is $180 - 0.5 \times 10^{3-2} = 180 - 5 = 175$ metres. - The upper bound is $180 + 5 = 185$ metres. - For $t = 7.2$ (2 s.f.), the lower bound is $7.2 - 0.05 = 7.15$ seconds. - The upper bound is $7.2 + 0.05 = 7.25$ seconds. 3. **Calculate lower bound of $s$:** Speed is lowest when distance is minimum and time is maximum: $$s_{lower} = \frac{d_{lower}}{t_{upper}} = \frac{175}{7.25} \approx 24.138$$ Rounded to 3 significant figures: $24.1$ m/s. 4. **Calculate upper bound of $s$:** Speed is highest when distance is maximum and time is minimum: $$s_{upper} = \frac{d_{upper}}{t_{lower}} = \frac{185}{7.15} \approx 25.874$$ Rounded to 3 significant figures: $25.9$ m/s. 5. **Final answer:** The lower bound of speed $s$ is $24.1$ m/s and the upper bound is $25.9$ m/s.