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

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Accepted Answer

"Given ${{dM\left( t \right)} \over {dt}}$ = bv²(t)

In free space no external force so there in only thrust force on rocket.

F_thrust = v${{dm} \over {dt}}$

Force on satellite = $- \overrightarrow v {{dm\left( t \right)} \over {dt}}$

M(t)a = – v (bv²)

$\Rightarrow$ a = $- {{b{v^3}} \over {M\left( t \right)}}$"

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

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

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Drill 25 more like these. Every day. Free.

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