The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric center, what would be the kinetic energy of one of the tires, in Joules, at the end of the run?

Cant quite get started.

To find the kinetic energy of one tire at the end of the run, we need to calculate its velocity first. We can use the formula for average velocity:

Average velocity (v) = Distance (d) / Time (t)

Given that the car covers 0.25 miles in 15 seconds, we first need to convert 0.25 miles to meters, as SI units are commonly used in scientific calculations.

1 mile = 1609.34 meters

Therefore, 0.25 miles = 0.25 * 1609.34 meters ≈ 402.34 meters

Now, let's find the average velocity:

v = d / t = 402.34 meters / 15 seconds ≈ 26.82267 meters/second

Since the tire rotates when the car is in motion, it covers a linear distance equal to the circumference of the rim. We can calculate the circumference using the diameter:

Circumference (C) = π * Diameter

Given that the diameter of the rim and tire is 46 cm, we convert it to meters:

1 cm = 0.01 meters

Therefore, the diameter of the rim and tire is 46 cm * 0.01 meters/cm = 0.46 meters

Now, let's find the circumference:

C = π * 0.46 meters

Next, we need to find how many rotations the tire makes during the run. We can divide the distance covered by the circumference to get the number of rotations.

Number of rotations = Distance covered / Circumference

Number of rotations = 402.34 meters / (π * 0.46 meters) ≈ 285.805 rotations

Now that we know the number of rotations, we can calculate the distance traveled by one rotation:

Distance covered per rotation = Circumference

Finally, we can find the linear velocity of the tire on its outer edge using the formula:

Linear velocity = Distance covered per rotation * Number of rotations / Time

Linear velocity = Circumference * 285.805 rotations / 15 seconds

Now that we have the linear velocity, we can calculate the kinetic energy of the tire using the formula:

Kinetic energy (K.E.) = 0.5 * Mass * Velocity^2

Since the rim and tire are treated as a solid disk that rotates through its geometric center, we need to consider the rotational kinetic energy as well. The formula for rotational kinetic energy is:

Rotational kinetic energy = 0.5 * Moment of inertia * Angular velocity^2

The moment of inertia for a disk is given by:

Moment of inertia (I) = 0.5 * Mass * Radius^2

Since the rim and tire have the same mass and we know the diameter, we can find the radius:

Radius of the rim and tire = Diameter / 2

Once we have the radius, we can calculate the moment of inertia.

Finally, we can add the kinetic energy and the rotational kinetic energy to get the total kinetic energy of the tire.