A car travels at a constant speed around a circular track whose radius is 2.1 km. The car goes once around the track in 320 s. What is the magnitude of the centripetal acceleration of the car?

1 m/s2

To find the magnitude of the centripetal acceleration of the car, we can use the formula for centripetal acceleration:

a = (v^2) / r

Where:
a = centripetal acceleration
v = velocity of the car
r = radius of the circular track

First, we need to find the velocity of the car. We know that the car goes once around the track in 320 seconds, so we can calculate the average velocity using:

v = (2 * π * r) / t

Where:
v = velocity of the car
π = 3.14159 (approximately)
r = radius of the circular track
t = time taken to complete one lap

Plugging in the values:

v = (2 * 3.14159 * 2.1 km) / 320 s

Note that the radius needs to be converted to the same units as the velocity. Let's convert kilometers to meters:

v = (2 * 3.14159 * 2100 m) / 320 s
v = (6.28318 * 2100 m) / 320 s
v ≈ 41.284 m/s

Now that we have the velocity, we can calculate the centripetal acceleration:

a = (v^2) / r

a = (41.284 m/s)^2 / 2.1 km

Again, the radius needs to be converted to meters:

a = (41.284 m/s)^2 / (2.1 km * 1000 m/km)
a = 41.284^2 m^2/s^2 / 2100 m

Calculating the value:

a ≈ 0.810 m/s^2

So, the magnitude of the centripetal acceleration of the car is approximately 0.810 m/s^2.

To find the magnitude of the centripetal acceleration of the car, we can use the formula for centripetal acceleration:

ac = v^2 / r

Where:
ac = centripetal acceleration
v = velocity of the car
r = radius of the circular track

Given that the car travels at a constant speed and goes once around the track in 320 s, we can calculate the velocity of the car.

v = distance / time

The distance traveled is equal to the circumference of the circular track, which is equal to 2πr.

v = 2πr / t

Substituting the given values:
v = 2π(2.1 km) / (320 s)

Calculating the value of v:
v ≈ 0.0416 km/s

To find the centripetal acceleration, we need to convert the velocity to meters per second:

v = 0.0416 km/s * (1000 m/km) / (3600 s/h)

v ≈ 11.56 m/s

Now, substituting the values of v and r into the formula for centripetal acceleration:

ac = (11.56 m/s)^2 / (2.1 km)

Converting the radius to meters:
ac = (11.56 m/s)^2 / (2.1 km * 1000 m/km)

Calculating the value of ac:
ac ≈ 66.88 m/s^2

Therefore, the magnitude of the centripetal acceleration of the car is approximately 66.88 m/s^2.