An energy-absorbing car bumper with its springs initially undeformed has an equivalent s...

An energy-absorbing car bumper with its springs initially undeformed has an equivalent spring constant of 3000 lb/in. If the 2500-lb car approaches a massive wall with a speed of 5 mi/hr, determine (a) the velocity v of the car as a function of time during contact with the wall, where t=0 is the beginning of the impact, and (b) the maximum deflection x_max of the bumper.