Frame \(A\) moves with constant velocity \(v_0\) relative to the ground along a straight line. At time \(t = 0\), the origins of frame \(A\) and frame \(B\) coincide at \(x = 0\), and frame \(B\) is at rest relative to frame \(A\). Frame \(B\) accelerates relative to frame \(A\) with acceleration \(a_{B/A}(t) = bt\), where \(b\) is a positive constant. Which of the following expressions represents the position of the origin of frame \(B\) relative to the ground, \(x_{B/G}(t)\), as a function of time \(t\)?