a) Convert $10 \mathrm{~km} / \mathrm{h}^{2}$ to $\mathrm{mm} / \mathrm{s}^{2}$ by giving your answer in standard form.

Step 1 ：We have $10 \text{ km/h}^2 = 10 \times 1000 \text{ m/h}^2 = 10000 \text{ m/h}^2$

Step 2 ：We know that $1 \text{ hour} = 3600 \text{ seconds}$, so $10000 \text{ m/h}^2 = 10000 \times (1/3600)^2 \text{ m/s}^2$

Step 3 ：So, $10000 \text{ m/h}^2 = 10000 \times (1/3600)^2 \text{ m/s}^2 = 0.07716 \text{ m/s}^2$

Step 4 ：Finally, we convert meters to millimeters, $0.07716 \text{ m/s}^2 = 0.07716 \times 1000 \text{ mm/s}^2 = \boxed{77.16} \text{ mm/s}^2$