A car travels at a constant speed around a circular track whose radius is 3.94km. The car goes once around the track in 260s. What is the magnitude of the centripetal acceleration of the car?
The magnitude of centripetal acceleration can be calculated using 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 track.
To find the velocity, we need to calculate the distance traveled by the car in one lap. The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius.
So, the distance traveled by the car in one lap is:
d = C = 2πr = 2 × π × 3.94km
To find the velocity, we divide the distance by the time:
v = d / t = (2 × π × 3.94km) / 260s
Now we can substitute the values in the formula for centripetal acceleration:
ac = v^2 / r = ((2 × π × 3.94km) / 260s)^2 / 3.94km
Simplifying the expression:
ac = ((2 × π × 3.94)^2 / 260^2) km/s^2
Calculating the expression:
ac ≈ 0.009860 km/s^2
Therefore, the magnitude of the centripetal acceleration of the car is approximately 0.009860 km/s^2.