Final answer:
Using the formula for angular deceleration, with the provided values, results in a negative angular velocity, which indicates the propeller has stopped and reversed direction, a situation that is not reasonable for an aircraft propeller. None of the given options are correct.
Step-by-step explanation:
The subject of the question is Physics, and it is at a high school level. To solve for the rotation rate of the propeller after 40 seconds, we can use the formula for angular deceleration, which is ω = ω0 - αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular deceleration, and t is the time in seconds.
Given that the initial rotation rate is 10 rev/s, we first need to convert this rate to radians per second. Since 1 revolution is equivalent to 2π radians, we have ω0 = 10 rev/s × 2π rad/rev = 20π rad/s.
The angular deceleration is given as α = 2.0 rad/s2. Substituting these values into the equation gives us ω = 20π rad/s - (2.0 rad/s2 × 40 s) = 20π rad/s - 80 rad/s.
However, because this calculation results in a negative number for ω, it means that the propeller has completely stopped and even reversed direction, which is not a reasonable situation for an aircraft propeller.
Therefore, the rotation rate of the propeller after 40 seconds cannot be a positive number like the ones given in options (a) 30 rev/s, (b) 90 rev/s, or (c) 50 rev/s.
Option (d) 10 rev/s is also incorrect because the propeller decelerates. The mistake in this problem is either in the calculation or the premise; the aircraft propeller would never reverse direction under a constant deceleration condition.