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 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

Question

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 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, − 2 α v 2 M, − α v 2 M, − α v 2 2 M, − α v 2

MARKS App · Accepted Answer

d M d t = α v F thrust = - v d M d t = M a ⇒ - v α v = M a ⇒ a = − α v 2 M

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