An experimental rover is tested on a long, straight, horizontal track. In the first trial, the rover starts from rest and undergoes a constant acceleration \(a_0\) for a time interval \(t_0\), resulting in a displacement \(\Delta x_1\). In the second trial, the rover again starts from rest but undergoes a constant acceleration \(2a_0\) for a time interval \(2t_0\), resulting in a displacement \(\Delta x_2\). What is the value of the displacement \(\Delta x_2\) in terms of \(\Delta x_1\)?