A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 260 km/h in a semicircular arc with a radius of 210 m.

Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.

If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding?

To determine the tangential and radial acceleration of the car, we can use the following formulas:

Tangential acceleration (at) = (Change in velocity) / (Change in time)
Radial acceleration (ar) = (Tangential acceleration)^2 / (Radius of curvature)

Step 1: Convert the given speed from km/h to m/s.
Speed in m/s = (Speed in km/h) * (1000 m/1 km) * (1 hr/3600 s)

Let's calculate:
Speed in m/s = 260 km/h * (1000 m/1 km) * (1 hr/3600 s) = 72.22 m/s

Step 2: The car accelerates from rest to a speed of 72.22 m/s, so the change in velocity is 72.22 m/s.

Step 3: The time it takes for the car to reach this speed is not given. Therefore, we will need additional information to calculate the tangential acceleration.

Now, let's move on to the second part of the question.

If the curve were flat (no elevation change), the only force acting in the radial direction would be the force of static friction between the tires and the road. To prevent slipping or skidding, static friction needs to provide the necessary radial acceleration.

The formula for the maximum static friction force (Fstatic) is:

Fstatic = mass * radial acceleration

We need to determine the coefficient of static friction (μstatic) between the tires and the road, which is defined as:

μstatic = Fstatic / (mass * gravitational acceleration)

To find μstatic, we need to cancel out the mass. Therefore, the actual value of mass is not required.

Rearranging the above equation, we get:

μstatic = radial acceleration / gravitational acceleration

Step 4: Calculate the radial acceleration using the formula mentioned above.

Radial acceleration = (Tangential acceleration)^2 / Radius of curvature

From Step 3, we obtained the tangential acceleration as (Change in velocity) / (Change in time). Since we don't know the time, we will not be able to calculate the tangential acceleration accurately. Therefore, we cannot find the radial acceleration and subsequently the coefficient of static friction without additional information.

To complete the calculation, we would need the time it took for the car to reach the given speed or any other relevant information that could help us find the tangential acceleration.