A space-ship travelling in the interstellar medium is picking up dust at a rate d M d t = α v , where α is a…

A space-ship travelling in the interstellar medium is picking up dust at a rate dMdt=αv, where α is a positive constant, v is the instantaneous velocity and M is the total mass of the space-ship at any instant. The instantaneous acceleration of the space-ship is

  1.   −2α v 2 M

  2.   −α v 2 M

  3.   −α v 2 2M

  4.   −α v 2

Solution

  dMdt=αv

Fthrust=-vdMdt=Ma

⇒-vαv=Ma

⇒a=−αv2M

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