A 1596 kg car traveling at 24.91 m/s skids to a halt. What is the change in the combined thermal energy of the car and the road surface?

To determine the change in the combined thermal energy of the car and the road surface, we need to calculate the initial and final kinetic energies of the car.

First, let's find the initial kinetic energy (KEi) of the car. The formula to calculate kinetic energy is:

KE = 1/2 * m * v^2

Where:
KE is the kinetic energy,
m is the mass of the car (1596 kg), and
v is the initial velocity of the car (24.91 m/s).

So, the initial kinetic energy (KEi) of the car is:

KEi = 1/2 * 1596 kg * (24.91 m/s)^2

Now, let's find the final kinetic energy (KEf) of the car. Since the car comes to a complete stop, the final velocity (vf) is 0 m/s. Hence, the final kinetic energy can be calculated as:

KEf = 1/2 * 1596 kg * (0 m/s)^2

Given that the final velocity (vf) is zero, the final kinetic energy (KEf) will also be zero.

The change in the kinetic energy (∆KE) is given by the difference between the initial and final kinetic energies:

∆KE = KEf - KEi

∆KE = 0 - (1/2 * 1596 kg * (24.91 m/s)^2)

Simplifying further:

∆KE = - (1/2 * 1596 kg * (24.91 m/s)^2)

This value is negative because the car's kinetic energy decreases as it comes to a halt.

Now, let's address the question of the change in combined thermal energy. During the skidding process, the friction between the car's tires and the road surface converts the car's kinetic energy into thermal energy, causing the car and road surface to heat up.

Hence, the change in the combined thermal energy is equal to the absolute value of the change in kinetic energy. Therefore, the change in the combined thermal energy of the car and the road surface would be:

∆Thermal Energy = |∆KE|

∆Thermal Energy = |-(1/2 * 1596 kg * (24.91 m/s)^2)|

We can plug the values into a calculator to find the final answer, which will be in joules (J).