A flat plate is moving normal to its plane through a gas under the action of constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?
[$A$] The resistive force experienced by the plate is proportional to $\mathrm{v}$
[$B$] The pressure difference between the leading and trailing faces of the plate is proportional to uv
[$C$] The plate will continue to move with constant non-zero acceleration, at all times
[$D$] At a later time the external force $F$ balances the resistive force.
IIT 2017, Advanced
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