Problem 1.355

The reference frame \(K^{\prime}\) moves in the positive direction of the \(x\) axis of the frame \(K\) with a relative velocity \(V\). Suppose that at the moment when the origins of coordinates \(O\) and \(O^{\prime}\) coincide, the clock readings at these points are equal to zero in both frames. Find the displacement velocity \(\dot{x}\) of the point (in the frame \(K\) ) at which the readings of the clocks of both reference frames will be permanently identical. Demonstrate that \(\dot{x}<V\).