A test sled on a straight track enters a braking zone at time \(t = 0\) with an initial speed \(v_0\) and experiences a time-dependent deceleration given by \(a(t) = -c t\), where \(c\) is a positive constant. The sled comes to rest after traveling a total stopping distance \(D_1\). If the sled enters the braking zone with an initial speed of \(3v_0\) under the same deceleration function, what is the new total stopping distance in terms of \(D_1\)?