Final answer:
The force needed to move the car at the maximum speed of 2 m/s cannot be determined based on the given information.
Step-by-step explanation:
First, let's calculate the spring constant of the wound-up spring toy car using Hooke's Law. Hooke's Law states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. The formula is F = kx, where F is the force, k is the spring constant, and x is the displacement. In this case, the initial spring length is 0.1 m and the spring is compressed until 0.02 m, so the displacement is 0.1 - 0.02 = 0.08 m. The mass of the car is 0.2 kg.
Using the given information, we can calculate the spring constant:
Force (F) = mass (m) * acceleration (a)
Using the formula for acceleration, a = (final velocity - initial velocity) / time. The initial velocity is 0 m/s, the final velocity is 2 m/s, and the time is not provided in the question, so we cannot calculate the force using this formula.
Therefore, we cannot determine the force needed to move the car at the maximum speed of 2 m/s based on the given information.