A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dM(t)dt=bv2(t) , where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

F=vreldMdt M(t) (a)=−v(bv2) a=−bv3M(t)

F=vreldMdt M(t) (a)=−v(bv2) a=−bv3M(t)

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A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{d M (t)}{d t} = b v^{2} (t)$ , where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

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$- \frac{b v^{3}}{M (t)}$

$- \frac{b v^{3}}{2 M (t)}$

$- b v^{3} (t)$

$- \frac{2 b v^{3}}{M (t)}$

answer is B.

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$F = v_{r e l} \frac{d M}{d t} M (t) (a) = - v (b v^{2}) a = \frac{- b v^{3}}{M (t)}$

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