Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_30

2/30 The cart impacts the safety barrier with speed \(v_0 = 3.25 \text{ m/s}\) and is brought to a stop by the nest of nonlinear springs which provide a deceleration \(a = -k_1x - k_2x^3\), where \(x\) is the amount of spring deflection from the undeformed position and \(k_1\) and \(k_2\) are positive constants. If the maximum spring deflection is \(475 \text{ mm}\) and the velocity at half-maximum deflection is \(2.85 \text{ m/s}\), determine the values and corresponding units for the constants \(k_1\) and \(k_2\).