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A rocket-driven car of total mass M loses mass at a constant rate λ per unit of time at a constant ejection speed V relative to the car. If the total resistance to motion is kv with the speed is v, show that the acceleration of the car along a straight horizontal road is (λV-kv) /(M- λt) at time t from the start. Hence show that the speed from rest is (λ V/k)[1-(1- λ t/M)^(k/λ)].

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