Question Number 28382 by Ruchinna1 last updated on 25/Jan/18
$${A}\:{boat}\:{of}\:{mass}\:{m},\:{traveling}\:{with}\:{v}\:{of}\:{Vo}\:{at} \\ $$$${t}=\mathrm{0}.\:{A}\:{power}\:{is}\:{shut}\:{off}\:{assuming}\:{water}\: \\ $$$${resistance}\:{is}\:{proportioal}\:{to}\:{V}\hat {{n}}\:\:{and}\:{V}\:{is}\: \\ $$$${instantaneous}\:{velocity}\:{find}\:{V}\:{as}\:{a}\:{function} \\ $$$${of}\:{the}\:{distance}\:{travelled} \\ $$
Answered by ajfour last updated on 25/Jan/18
$$\frac{{VdV}}{{dx}}=−{kV} \\ $$$${V}−{V}_{\mathrm{0}} =−{kx} \\ $$$${V}={V}_{\mathrm{0}} −{kx} \\ $$