A car travels at a constant speed around a circular track whose radius is 2.60 km. The car goes once around the track in 344 s. What is the magnitude of the centripetal acceleration of the car?

speed=2PI*r/time

centripetal acceleration= speed^2/r

To find the magnitude of the centripetal acceleration of the car, we need to first determine the car's velocity and then use the formula for centripetal acceleration.

The formula for the speed of an object moving in a circle is:

v = 2πr / T,

where:
- v is the speed of the object,
- π is a mathematical constant approximately equal to 3.14159,
- r is the radius of the circular track, and
- T is the time it takes for the object to complete one revolution or go around the track once.

In this case, the radius of the circular track, r, is given as 2.60 km, and the time it takes for the car to complete one revolution around the track, T, is given as 344 s.

Plugging these values into the formula, we get:

v = 2π(2.60 km) / 344 s.

To convert kilometers to meters, multiply the value by 1000.

v = 2π(2.60 km) / 344 s * 1000 m/km.

Simplifying this expression, we have:

v = 2π(2.60 km / 344 s * 1000).

Now, calculate the value of v.

Then, once you have the speed, you can use the formula for centripetal acceleration:

a = v^2 / r,

where:
- a is the magnitude of the centripetal acceleration,
- v is the speed of the object, and
- r is the radius of the circular track.

Plug in the values of v and r and calculate the magnitude of the centripetal acceleration, a.