To find the missile's average acceleration in multiples of $g$ (where $g = 9.80 \, \text{m/s}^2$), follow these steps:

1. Convert the speed from km/s to m/s:

$6.3 \, \text{km/s} = 6300 \, \text{m/s}$

2. Calculate the acceleration:

$a = \frac{\Delta v}{\Delta t} = \frac{6300 \, \text{m/s}}{55 \, \text{s}} \approx 114.55 \, \text{m/s}^2$

3. Express this acceleration as a multiple of $g$:

$\text{Multiple of } g = \frac{114.55 \, \text{m/s}^2}{9.80 \, \text{m/s}^2} \approx 11.69$

So, the missile's average acceleration is approximately 11.69 times the acceleration due to gravity $g$.

Would you like further details or have any questions?

Here are some related questions:

1. How does this acceleration compare to that of other vehicles, like fighter jets?
2. What would be the missile's speed after 30 seconds?
3. How far would the missile travel during this acceleration period?
4. How does this acceleration impact the structure of the missile?
5. How does this acceleration relate to the forces experienced by the payload?

Tip: When working with very large or very small values, always check unit conversions to maintain accuracy.