A bungee cord stretches 2-4 times their unstretched length, and a jumper feels no more than 2.5-3.5g of acceleration. Assume the force in the cord has the math form kP -BP^3 , where k and B are constants and P is the amount of stretch in the cord past the unstretched length. Design a cord (design the constants k and B so the cord stretches 2.5 times the unstretched length, and the acceleration of the jumper doesn't exceed 3g, and the cord has zero stiffness at the bottom of a 400ft drop

I know I have to use work energy principle. I am stuck on whether or not the kinetic energy at the bottom of the drop is zero or if it exists as 0.5mv^2? Also, is the force in the cord the work in the equation?

I just want some advice on how to go about this, a direct answer is not needed. Thanks, I'd really appreciate it!

Why did you add another P in your integral?