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A particle is initially at the origin and at rest. It starts to move along a straight line with acceleration \(a(t) = \frac{6}{(t+1)^2}\) m/s\(^2\), for \(t \ge 0\).
Find the velocity function \(v(t)\) of the particle.
How long will it take for the particle to reach a speed of 4 m/s?
How far will the particle have travelled in this time?
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