A 2570-lb test car moving with velocity v0 = 5 mi/h collides with a rigid barrier at t = 0...

A 2570-lb test car moving with velocity v0 = 5 mi/h collides with a rigid barrier at t = 0. As a result of the behavior of its energy-absorbing bumper, the response of the car to the collision can be simulated by the damped spring–mass oscillator shown with k = 8000 lb/ft and c = 3000 lb-s/ft. Assume that the mass is moving to the left with velocity v0 = 5 mi/h and the spring is unstretched at t = 0. Determine the car's deceleration (a) immediately after it contacts the barrier: (b) at t = 0.04 s: and (c) at t = 0.08 s.