You devise a wind-up car powered by a spring for trips to the grocery store. The car has an inertia of \(500 \mathrm{~kg}\) and is \(4.2 \mathrm{~m}\) long. It should be able to accelerate from rest to \(20 \mathrm{~m} / \mathrm{s}\) at least 50 times before the spring needs winding. The spring runs the length of the car, and a full winding compresses it to half this length. In order to meet the acceleration requirement, what must the value of the spring constant be?