Question: 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

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?

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