A body of initial mass m₀ is on a smooth horizontal surface. Its mass decreases exponentially with decay constant λ by ejecting mass backward at constant relative speed u. It starts from rest. Find its speed after time t.
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Question

A body of initial mass m₀ is on a smooth horizontal surface. Its mass decreases exponentially with decay constant λ by ejecting mass backward at constant relative speed u. It starts from rest. Find its speed after time t.

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G1 Physics · Accepted Answer

Step 1: For a variable-mass body, m dv = −u dm. Step 2: With m=m₀exp(−λt), dm/m=−λdt, so dv=uλdt. Step 3: Starting from rest gives v=uλt. Correct answer: A.