Help plz show work A 8,000-kg freight car rolls along rails with negligible fric

Question

Help plz show work

A 8,000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants k1 = 1,500 N/m and k2 = 3,300 N/m. After the first spring compresses a distance of x1 = 33.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest x2 = 52.5 cm after first contacting the two-spring system. Find the car's initial speed.

Explanation / Answer

energy conservation

1/2 m v^2 = 1/2 k1 *(x2)^2 + 1/2 k2 (x2-x1)^2

x1=0.33; x2 =0.525

v=0.26 m/s

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