A particle moves in one dimension along the positive \(x\)-axis. Starting at position \(x = 0\) with an initial speed \(v_0\) in the \(+x\)-direction, the particle experiences an acceleration given by \(a(x) = -\beta x^2\), where \(\beta\) is a positive constant. Which of the following expressions represents the distance \(D\) the particle travels before momentarily coming to rest?