A 615 kg racing car completes one lap in 14.3 s around a circular track with a radius of 40.0 m. The car moves at constant speed.
(a) What is the acceleration of the car?
a= (4pi^2r)/T2
=(4pi^2(50))/(14.3)^2
=9.7 m/s^2
To find the acceleration of the car, we can use the following formula:
Acceleration (a) = (v^2) / r
where:
v = velocity of the car
r = radius of the circular track
Since the car moves at a constant speed, the velocity can be determined using the formula:
v = 2πr / t
where:
t = time taken to complete one lap
Plugging in the given values:
t = 14.3 s
r = 40.0 m
We can now find the velocity:
v = 2π(40.0) / 14.3
v ≈ 8.879 m/s
Now, let's find the acceleration:
a = (v^2) / r
a = (8.879)^2 / 40.0
a ≈ 1.961 m/s^2
Therefore, the acceleration of the car is approximately 1.961 m/s^2.
To find the acceleration of the car, we need to use the equation for centripetal acceleration:
ac = v^2 / r
where:
- ac represents the centripetal acceleration
- v represents the velocity of the car
- r represents the radius of the circular track
Given:
- The car completes one lap in 14.3 seconds, which can be used to find the velocity of the car.
- The radius of the circular track is 40.0 meters.
To find the velocity, we can use the formula:
v = 2πr / t
where:
- v represents the velocity
- r represents the radius of the circular track
- t represents the time taken to complete one lap
Substituting the given values:
v = (2 * π * 40.0 m) / 14.3 s
Calculating this, we find:
v ≈ 87.965 m/s
Now, substitute this value of velocity into the formula for centripetal acceleration:
ac = (87.965 m/s)^2 / 40.0 m
Calculating this, we find:
ac ≈ 192.908 m/s^2
Therefore, the acceleration of the car is approximately 192.908 m/s^2.