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  4. A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate ( dM ( t )/ dt )= bv 2( t ), where v ( t ) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

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Q. 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:

JEE MainJEE Main 2020Laws of Motion

Solution:

$\frac{ dm ( t )}{ dt }= bv ^{2}$
$F _{\text {thast }}= v \frac{ dm }{ dt }$
Force on statellite $=-\vec{ v } \frac{ dm ( t )}{ dt }$
$M(t) a=-v\left(b v^{2}\right)$
$a = a \frac{ bv ^{3}}{ M ( t )}$
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