Find speed when fuel exhausted

A question is this type if and only if it asks specifically for the speed of a rocket or vehicle at the instant all fuel has been burnt, after first obtaining a general expression for velocity.

1 questions · Challenging +1.8

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Edexcel M5 Q3

7 marks Challenging +1.8

A rocket propels itself by its engine ejecting burnt fuel. Initially the rocket has total mass \(M\), of which a mass \(kM\), \(k < 1\), is fuel. The rocket is at rest when its engine is started. The burnt fuel is ejected with constant speed \(c\), relative to the rocket, in a direction opposite to that of the rocket's motion. Assuming that there are no external forces, find the speed of the rocket when all its fuel has been burnt. [7]