Discussion
An accelerometer has a bias of \( 0.001 \ \mathrm{m/s^2} \). Integrated twice over 60 seconds the position error is
Answer: B
Correct answer: 1.8 m
A constant acceleration error integrates twice into a position error growing with the square of time:
\[ \Delta x = \tfrac{1}{2} a t^2 = \tfrac{1}{2} \times 0.001 \times 60^2 = \tfrac{1}{2} \times 0.001 \times 3600 = 1.8\ \mathrm{m} \]
The distractor \( 3.6 \) omits the factor of one half, and \( 0.06 \) integrates only once, giving the velocity error instead. This quadratic growth is precisely why an attitude and heading reference system does not attempt to output position: a bias too small to matter for attitude becomes tens of metres within minutes.
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