A satellite in force free space sweeps stationery interplanetary dust at a rate dm/ dt = av where m is the mass v is the velocity of the satellite and a is constant.What is the deceleration of the satellite

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Solution

$\frac{d m}{d t} = a v$
But force is given by, $F_{t} = - v \frac{d m}{d t} = (a v) v = - a v^{2}$
Decelaration of satellite is $a^{'} = \frac{F t}{m} = - \frac{a v^{2}}{m}$

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A satellite in force free space sweeps stationery interplanetary dust at a rate dm/ dt = av where m is the mass v is the velocity of the satellite and a is constant.What is the deceleration of the satellite

dmdt=avBut force is given by, Ft=−vdmdt=(av)v=−av2Decelaration of satellite is a′=Ftm=−av2m

$\frac{d m}{d t} = a v$
But force is given by, $F_{t} = - v \frac{d m}{d t} = (a v) v = - a v^{2}$
Decelaration of satellite is $a^{'} = \frac{F t}{m} = - \frac{a v^{2}}{m}$