Students set up an experiment with a model rocket in a wind tunnel. The wind tunnel is programmed to produce a time-varying force that accelerates the rocket along a horizontal, low-friction guide wire. The acceleration \(a\) of the rocket model varies with time \(t\) according to the equation \(a(t) = c\sqrt{t}\), where \(c\) is an unknown positive constant and \(t \ge 0\). The rocket starts from rest at \(x = 0\) when \(t = 0\).