A car travels at a constant speed around a circular track whose radius is 2.82 km. The car goes once around the track in 364 s. What is the magnitude of the centripetal acceleration of the car?
To find the magnitude of the centripetal acceleration of the car, we can use the formula:
a = V^2 / r
Where:
a is the centripetal acceleration
V is the linear velocity of the car
r is the radius of the circular track
Given that the car goes once around the track in 364 s, we can calculate the linear velocity using the formula:
V = 2πr / t
Where:
t is the time taken to complete one revolution
Substituting the given values:
V = (2π * 2.82 km) / 364 s
Calculating V:
V = (2π * 2.82 km) / 364 s ≈ 0.612 km/s
Substituting the calculated value of V and the given radius in the formula for acceleration:
a = (0.612 km/s)^2 / 2.82 km
Calculating a:
a = (0.612^2 km^2/s^2) / 2.82 km ≈ 0.133 km/s^2
Therefore, the magnitude of the centripetal acceleration of the car is approximately 0.133 km/s^2.
To find the magnitude of the centripetal acceleration, we can use the formula:
ac = (v^2) / r
Where ac is the centripetal acceleration, v is the velocity of the car, and r is the radius of the circular track.
First, let's find the velocity of the car. We know that the car goes once around the track in 364 s, so we can find the velocity using the formula:
v = (2 * π * r) / t
Where v is the velocity, π is pi (approximately 3.14159), r is the radius of the circular track, and t is the time it takes to go once around the track.
In this case, the radius of the track is given as 2.82 km, and the time it takes to go once around the track is given as 364 s.
Now we can substitute these values into the formula to find the velocity:
v = (2 * π * 2.82) / 364
Calculating this expression, we find that the velocity is approximately 0.0516 km/s.
Now that we have the velocity, we can find the magnitude of the centripetal acceleration by substituting the values into the formula:
ac = (v^2) / r
ac = (0.0516)^2 / 2.82
Calculating this expression, we find that the magnitude of the centripetal acceleration is approximately 0.000948 km/s^2.