A cart of mass \(m = 2.0 \text{ kg}\) moves along a straight horizontal track. A sensor measures the net force \(F(t)\) applied to the cart during an interaction, as shown in the force-versus-time graph. The force increases quadratically from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\) according to \(F(t) = c t^2\), reaching a maximum value of \(18 \text{ N}\) at \(t = 3.0 \text{ s}\), after which the force drops instantly to zero. What is the average force \(F_{\text{avg}}\) exerted on the cart during the time interval from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\)?