Final answer:
The linear acceleration of the car is 3.72 m/s^2. The tires make 3.11 revolutions in 2.50 seconds. The final angular velocity of the tires is 38.75 rad/s and the final velocity of the car is 9.30 m/s.
Step-by-step explanation:
(a) To calculate the linear acceleration of a car, we can use the formula:
a = r × α
Where a is the linear acceleration, r is the radius of the tires, and α is the angular acceleration. Plugging in the given values, we have:
a = (0.240 m) × (15.5 rad/s2) = 3.72 m/s2
(b) To find the number of revolutions the tires make in 2.50 seconds, we can use the formula:
n = α × t / 2π
Where n is the number of revolutions, α is the angular acceleration, t is the time, and 2π is the number of radians in one revolution. Plugging in the given values, we have:
n = (15.5 rad/s2) × (2.50 s) / (2π) = 3.11 revolutions
(c) To calculate the final angular velocity of the tires, we can use the formula:
ωf = ωi + α × t
Where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. Since the initial angular velocity is not given, we assume it to be zero. Plugging in the given values, we have:
ωf = 0 + (15.5 rad/s2) × (2.50 s) = 38.75 rad/s
(d) To find the final velocity of the car, we can use the formula:
v = r × ω
Where v is the final velocity, r is the radius of the tires, and ω is the final angular velocity. Plugging in the given values, we have:
v = (0.240 m) × (38.75 rad/s) = 9.30 m/s