Convert an acceleration of 10 ms⁻² in km h⁻².

The correct option is 1.29 x 10⁵ km h⁻².

To convert acceleration from meters per second squared (${\text{ms}}^{-2}$) to kilometers per hour squared (${\text{km h}}^{-2}$), we can convert the units of length and time individually.

First, let us establish the conversion factors for distance and time:
1. Convert meters (m) to kilometers (km):
$$1\text{m}=\frac{1}{1000}\text{km}={10}^{-3}\text{km}$$
2. Convert seconds (s) to hours (h):
$$1\text{s}=\frac{1}{3600}\text{h}$$

Now, let us write the expression for acceleration and substitute the conversion factors:
$$a=10\text{m}\cdot {\text{s}}^{-2}=10���\frac{\text{m}}{{\text{s}}^2}$$
Substituting $\text{1 m}={10}^{-3}\text{km}$ and $\text{1 s}=\frac{1}{3600}\text{h}$ into the equation:
$$a=10\cdot \frac{{10}^{-3}\text{km}}{{\left(\frac{1}{3600}\text{h}\right)}^2}$$

Simplifying the denominator:
$${\left(\frac{1}{3600}\right)}^2=\frac{1}{3600\cdot 3600}=\frac{1}{12960000}$$

Substitute this back into the acceleration formula:
$$a=10\cdot {10}^{-3}\cdot 12960000\text{km}\cdot {\text{h}}^{-2}$$
Simplifying the values:
$$a={10}^{-2}\cdot 12960000\text{km}\cdot {\text{h}}^{-2}$$
$$a=129600\text{km}\cdot {\text{h}}^{-2}$$

Expressing the result in scientific notation:
$$a=1.296\cdot {10}^5\text{km}\cdot {\text{h}}^{-2}\approx 1.29\cdot {10}^5\text{km}\cdot {\text{h}}^{-2}$$

Therefore, the converted acceleration is $1.29\cdot {10}^5\text{km}\cdot {\text{h}}^{-2}$.