A car travels at a constant speed around a circular track whose radius is 3.5 km.The car goes once around the track in 400 s.What is the magnitude of the centripetal acceleration of the car?

v^2/r

v = 2 pi r /T = 2 pi (3500/400)

v = 55 m/s

v^2/r = 55^2/3500 = .864 m/s^2

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

a = v^2 / r,

where:
- a represents the centripetal acceleration,
- v represents the velocity of the car, and
- r represents the 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 400 seconds, so we can calculate the velocity using:

v = 2πr / t,

where:
- π represents the constant pi, and
- t represents the time taken to complete one lap or revolution.

Plugging in the values, we have:

v = (2π * 3.5 km) / 400 s.

Now, let's calculate the velocity:

v = (2 * 3.14 * 3.5 km) / 400 s,
= (6.28 * 3.5 km) / 400 s,
≈ 0.0549 km/s.

Note: We usually prefer to work with SI units (meters and seconds) in physics. So, let's convert kilometers to meters:

v = 0.0549 km/s * 1000 m/km,
≈ 54.9 m/s.

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

a = (54.9 m/s)^2 / 3.5 km.

Again, let's convert the kilometer into meters:

a = (54.9 m/s)^2 / (3.5 km * 1000 m/km),
= (54.9 m/s)^2 / 3500 m,
≈ 0.8564 m/s^2.

Therefore, the magnitude of the centripetal acceleration of the car is approximately 0.8564 m/s^2.

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 is the centripetal acceleration
- v is the velocity
- r is the radius

Given that the car travels at a constant speed and goes once around the track in 400 seconds, we can find the velocity by dividing the total distance traveled by the time taken.

Since the car goes once around a circular track, the distance traveled is the circumference of the track, given by 2πr.

Let's calculate the velocity first:

Distance traveled = circumference of track = 2π × 3.5 km
= 2 × 3.14 × 3.5 km
≈ 21.98 km

Velocity (v) = Distance / Time
= 21.98 km / 400 s
≈ 0.05495 km/s

Now, we can calculate the centripetal acceleration:

Centripetal Acceleration (a) = v^2 / r
= (0.05495 km/s)^2 / 3.5 km
≈ 0.000958 km/s^2

Therefore, the magnitude of the centripetal acceleration of the car is approximately 0.000958 km/s^2.