Final answer:
The question asks for the calculation of the angular acceleration and total revolutions of an automobile engine slowing from 3500 to 1200 rpm over 2.5 s. Angular acceleration is found using the change in angular velocity over time and converting rpm to radians per second. Total revolutions are calculated with the average angular velocity multiplied by time and converting the result from radians to revolutions.
Step-by-step explanation:
The question involves calculating the angular acceleration and the total number of revolutions of an automobile engine that slows down from 3500 rpm to 1200 rpm in 2.5 seconds. To find the angular acceleration (assuming it is constant), we would use the formula α = (ωf - ωi) / t, where α is the angular acceleration, ωf is the final angular velocity in radians per second (rps), ωi is the initial angular velocity in rps, and t is the time in seconds. The angular velocities need to be converted from revolutions per minute (rpm) to rps first: ωi = 3500 rpm × (2π rad/rev) / (60 s/min) and ωf = 1200 rpm × (2π rad/rev) / (60 s/min).
To calculate the total number of revolutions the engine makes in this time, we can use the formula θ = (ωi + ωf)/2 × t, where θ is the total angle in radians and we then convert θ to revolutions.