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A rocket is launched from rest. It accelerates vertically according to the function \(a(t) = 2e^{-t/50}\) m/s\(^2\), for \(t \ge 0\).
Find the velocity function \(v(t)\) of the rocket.
How long will it take for the rocket to reach a speed of 80 m/s?
How far will the rocket have travelled in this time?
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