How Do You Calculate the Spring Constant for a Toy Car Accelerated by a Spring?

AI Thread Summary
To calculate the spring constant for a toy car accelerated by a spring, start with Hooke's Law, which relates force to displacement. The equation F = (1/2)kx^2 is relevant, where F is the force exerted by the spring, k is the spring constant, and x is the displacement. In this scenario, the force can also be derived from the car's mass and acceleration using Newton's second law, F = ma. By equating the two expressions for force, you can solve for the spring constant k. Properly applying these principles will yield the correct spring constant for the toy car.
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A 2.8 kg toy car at rest on a horizontal surface is accelerated by a spring to 4.5 m/s in a distance of 5.3 cm. What is the spring constant of the spring?

Hello, I was working on this problem in my homework but my professor hardly went over the spring constant in lecture. I was working on the problem but keep coming up with the incorrect answer.

Is starting off with F=(1/2)kx^2 the correct way to start off with this sort of problem?
 
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