Question
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{ dM ( t )}{ dt }= bv ^{2}( t ),$ where $v ( t )$ is its instantaneous velocity. The instantaneous acceleration of the satellite is
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Answer
$\frac{\operatorname{dm}( t )}{ dt }= bv ^{2}$
$F _{\text {thast }}= v \frac{ dm }{ dt }$
Force on statellile $=-\overrightarrow{ v } \frac{ dm ( t )}{ dt }$
$M ( t ) a =- v \left( bv ^{2}\right)$
$a = - \frac{ bv ^{3}}{ M ( t )}$
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