The power screw starts from rest and is given a rotational speed \(\dot{\theta}\) which increases uniformly with time \(t\) according to \(\dot{\theta}=k t\), where \(k\) is a constant. Determine the expressions for the velocity \(v\) and acceleration \(a\) of the center of ball \(A\) when the screw has turned through one complete revolution from rest. The lead of the screw (advancement per revolution) is \(L\).

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