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I attached the graph, provided in the problem, as a document.

This is the wording of the problem: A 5000-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 with k1 = 1700 N/m and k2 = 3500 N/m. After the first spring compresses a distance of 28.2 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 55.0 cm after first contacting the two-spring system. Find the car's initial speed.

I am trying to write a general formula for find the area under this curve. This is what I have come up with: [itex]\frac{1}{2}k_1x^2_1 + k_1x_1(x_2-x_1) + \frac{1}{2}[k_1x_2+k_2(x_2-x_1)](x_2-x_1)[/itex] But this just doesn't seem correct. The graph is rather confusing.

This is the wording of the problem: A 5000-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 with k1 = 1700 N/m and k2 = 3500 N/m. After the first spring compresses a distance of 28.2 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 55.0 cm after first contacting the two-spring system. Find the car's initial speed.

I am trying to write a general formula for find the area under this curve. This is what I have come up with: [itex]\frac{1}{2}k_1x^2_1 + k_1x_1(x_2-x_1) + \frac{1}{2}[k_1x_2+k_2(x_2-x_1)](x_2-x_1)[/itex] But this just doesn't seem correct. The graph is rather confusing.

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