If the box is initially at rest at x=0, what is its speed after it has traveled 17.0 m ?

A force in the +x-direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 5.40 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.

Net work done on the box equals its change in kinetic energy (Work-Energy Theorem):
1/2 m v^2 = ∫ F(x) dx
1/2* 5.40kg* v^2 = 18.0N * 17m – 1/2*0.530N/m*(17m)^2
2.70kg * v^2 = 229.4 N m
v^2 = 84.97 m^2/s^2
v = 9.22 m/s

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