physics spring problem?

Question

You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1300 car moving at 0.600 is to compress the spring no more than 7.40×10−2 before stopping.
What should be the force constant of the spring? Assume that the spring has negligible mass.

Answer 1

The energy required to stop the car is ∫f(x)*dx. The energy of the car is .5*m*v^2. These must be equal. For a linear spring, the force is f(x)= k*x, where k=spring constant. Therefore ∫k*xdx(0 to d)=.5*m*v^2, or .5*k*d^2=.5*m*v^2; k = (m*v^2)/d^2. Here d=7.4*10^-2, v=.600, and m=1300