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A spaceship in space sweeps stationary...

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

A

`-bv^(3)(t)`

B

`-(bv^(3))/(M(t))`

C

`-(2bv^(3))/(M(t))`

D

`-(bv^(3))/(2M(t))`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dm(t))/(dt)=bv^(2)`
`F_("thrust")=v(dm)/(dt)`
Force on satellite `=-vecv(dm(t))/(dt)`
`M(t)a=-v(bv^(2))`
`a=-(bv^(3))/(M(t))`
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