A railroad car that has an inertia of \(5.04 \times 10^{4} \mathrm{~kg}\) is moving to the right at \(4.25 \mathrm{~m} / \mathrm{s}\) when it collides and couples with three identical railroad cars that are already coupled together and moving in the same direction at \(2.09 \mathrm{~m} / \mathrm{s}\). If the acceleration of the single car is \(5.45 \mathrm{~m} / \mathrm{s}^{2}\) to the left while it is changing velocity, how long does the interaction take?