Force, $F = kv,\lbrack k\rbrack = \frac{\lbrack F\rbrack}{\lbrack v\rbrack} = \frac{\lbrack MlT^{- 2}\rbrack}{\lbrack LT^{- 1}\rbrack} = \left\lbrack MT^{- 1} \right\rbrack.$ So, unit is $kgs^{- 1}$
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