Final answer:
To find the number of revolutions the fan must make for its speed to decrease from 0.90 rev/s to 0.45 rev/s, we can use the equation Δω = (ωf - ωi) = -0.45 rev/s - 0.90 rev/s = -1.35 rev/s.
the fan is slowing down, the angular acceleration is negative. Using the equation ωf = ωi + αt, we can rearrange it to find the time it takes for the fan to slow down: t = (ωf - ωi) / α = (-1.35 rev/s - 0.90 rev/s) / α = -2.25 / α.
Correct options is 1 rev.
Step-by-step explanation:
To find the number of revolutions the fan must make for its speed to decrease from 0.90 rev/s to 0.45 rev/s, we can use the equation:
Δω = (ωf - ωi) = -0.45 rev/s - 0.90 rev/s = -1.35 rev/s
Since the fan is slowing down, the angular acceleration is negative. Using the equation ωf = ωi + αt, we can rearrange it to find the time it takes for the fan to slow down:
t = (ωf - ωi) / α = (-1.35 rev/s - 0.90 rev/s) / α = -2.25 / α
With the given options, none of them match the required number of revolutions the fan must make. Therefore, the correct answer is not listed.
To find the number of revolutions the fan must make for its speed to decrease from 0.90 rev/s to 0.45 rev/s, we need to consider the concept of uniform deceleration. Given that the answers for part a refer to speed changes per second, we might infer that the deceleration occurs in a constant rate over a one-second interval.
Therefore, if the fan is halving its speed from 0.90 rev/s to 0.45 rev/s, it's reasonable to assume that it takes one second for this change to occur. During this second, assuming uniform deceleration, the average speed of the fan would be the average of the initial and final speeds.
That would be (0.90 rev/s + 0.45 rev/s) / 2 = 0.675 rev/s. Multiplying this average speed by the time interval gives us the number of revolutions: 0.675 rev/s × 1 s = 0.675 revolutions. Since we've been given discrete answer choices and 0.675 is not one of them, the closest correct answer choice from the provided