Water waves of wavelength $ equire{cancel} ext{ } au $ and wave speed $ v $ are related by $ v = rac{ equire{cancel} ext{ } k}{ au} $ where $ k $ is a constant - AQA - A-Level Physics - Question 7 - 2020 - Paper 1

To isolate $k$, we can rearrange the formula as follows: $k = v imes au$

The SI unit for wave speed $v$ is meters per second (m/s), and the SI unit for wavelength $au$ is meters (m). Therefore, the units for $k$ can be determined:

$ext{Unit of } k = ext{Unit of } v imes ext{Unit of } au = ext{m/s} imes ext{m} = ext{m}^2/ ext{s}$

From the provided options, the unit $m^2 s^{-1}$ corresponds to the derived unit for $k$. Thus, the possible SI unit for $k$ is:

D $m^2 s^{-1}$