The tub of a washer goes into its spin-dry

cycle, starting from rest and reaching an angular speed of 2.9 rev/s in 8.5 s. At this point
the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 11.6 s.
Through how many revolutions does the
tub turn? Assume constant angular acceleration while it is starting and stopping.

To find the number of revolutions the tub of the washer turns, we can use the equations of rotational motion.

Let's break down the problem and find the angular acceleration (α), initial angular speed (ω0), final angular speed (ω), and time (t) for each phase of the motion.

Phase 1: Acceleration from rest to 2.9 rev/s
- Initial angular speed (ω0) = 0 (starting from rest)
- Final angular speed (ω) = 2.9 rev/s
- Time taken (t) = 8.5 s

Using the equation:
ω = ω0 + αt

Substituting the given values, we can solve for α:
2.9 rev/s = 0 + α(8.5 s)
α = 2.9 rev/s ÷ 8.5 s
α = 0.3412 rev/s^2

Phase 2: Deceleration from 2.9 rev/s to rest
- Initial angular speed (ω0) = 2.9 rev/s
- Final angular speed (ω) = 0 (slows to rest)
- Time taken (t) = 11.6 s

Using the same equation:
ω = ω0 + αt

Substituting the given values:
0 = 2.9 rev/s + α(11.6 s)
α = -2.9 rev/s ÷ 11.6 s
α = -0.2500 rev/s^2 (negative sign indicates deceleration)

Now that we have the values for α, ω0, ω, and t for both phases, we can find the total number of revolutions (θ) using the equation:

θ = ω0t + 1/2 αt^2 (for constant acceleration)

First, let's calculate the revolutions during acceleration (Phase 1):
θ1 = ω0t + 1/2 αt^2
θ1 = 0 + (1/2)(0.3412 rev/s^2)(8.5 s)^2
θ1 = 12.7845 rev

Next, let's calculate the revolutions during deceleration (Phase 2):
θ2 = ω0t + 1/2 αt^2
θ2 = 2.9 rev/s + (1/2)(-0.2500 rev/s^2)(11.6 s)^2
θ2 = 16.0208 rev

To find the total number of revolutions, we sum the revolutions during both phases:
Total revolutions = θ1 + θ2
Total revolutions = 12.7845 rev + 16.0208 rev
Total revolutions = 28.8053 rev

Therefore, the tub of the washer turns approximately 28.8053 revolutions during the given process.