A cart moves along a straight horizontal track with a velocity described by the function \(v(t) = v_0\left(1 - \dfrac{t}{\tau}\right)^3\), where \(v_0 = 16\text{ m/s}\) and \(\tau = 3.0\text{ s}\). The cart moves according to this relationship from \(t = 0\) to \(t = 2\tau = 6.0\text{ s}\). What is the total distance traveled by the cart from \(t = 0\) to \(t = 6.0\text{ s}\)?