Your approach to solving this problem is correct, but there may be an error in your calculations. Let's break down the problem and see if we can find where the mistake occurred.
First, we know that the car has a mass of 1500 kg and is traveling at a speed of 20 m/s. This means that the initial kinetic energy of the car is given by KE = 1/2 * m * v^2 = 1/2 * 1500 kg * (20 m/s)^2 = 300,000 J.
Next, we need to find the distance over which the car skids to a halt. This can be calculated using the formula x = v^2 / 2a, where v is the initial velocity and a is the deceleration due to friction. In this case, we can use the coefficient of rolling friction, μ = 0.02, to find the deceleration, a = μ * g (where g is the acceleration due to gravity, 9.8 m/s^2). Plugging in the values, we get a = 0.02 * 9.8 m/s^2 = 0.196 m/s^2. Now, we can solve for the distance, x = (20 m/s)^2 / (2 * 0.196 m/s^2) = 204.08 m.
Finally, we can calculate the change in thermal energy of the car and the road surface. Since the car has come to a complete stop, all of its initial kinetic energy has been converted into thermal energy through friction. Therefore, the change in thermal energy of the car is equal to the initial kinetic energy, ΔE = 300,000 J.
For the road surface, we can use the same approach. The friction between the car and the road surface causes the road to heat up, so the change in thermal energy for the road is also equal to the initial kinetic energy of the car, ΔE = 300,000 J.
It is possible that you made a mistake in your calculation of the distance, x. Double check your work and make sure you are using the correct values for the variables. Also, be sure to convert all units to SI units (meters, kilograms, seconds, etc.) before plugging them into equations. With the correct values, you should get the same answer of 300,000 J for the change in thermal energy for
