Answer
The force constant of the spring should be 63,000 N/m.
Work Step by Step
The potential energy stored in the spring will be equal to the car's kinetic energy.
$\frac{1}{2}kx^2 = \frac{1}{2}mv^2$
$k = \frac{mv^2}{x^2}$
$k = \frac{(1200~kg)(0.65~m/s)^2}{(0.090~m)^2}$
$k = 63,000~N/m$
The force constant of the spring should be 63,000 N/m.
