The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 9.58 s, at which time it is turning at 3.89 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 13.0 s. Through how many revolutions does the tub turn while it is in motion?

I have no idea how to solve this problem can someone help me please? Thank you very much

To solve this problem, we can use the equations of rotational motion. First, let's determine the initial angular velocity and final angular velocity of the tub.

Given:
Initial angular velocity, ω₁ = 0 rev/s (starting from rest)
Final angular velocity, ω₂ = 3.89 rev/s

Next, we need to find the time it takes for the tub to reach the final angular velocity (9.58 seconds) and the time it takes for the tub to come to rest (13.0 seconds). These will be useful in calculating the total angular displacement.

Using the equation for angular acceleration:

ω₂ = ω₁ + αt

Since the tub starts from rest, ω₁ = 0. Substituting the given values:

3.89 = 0 + α(9.58)

Simplifying the equation gives us the angular acceleration:

α = 3.89 / 9.58

Next, we can use the equation for angular displacement:

θ = ω₁t + 0.5αt²

Since ω₁ is 0 (starting from rest), the equation simplifies to:

θ = 0.5αt²

Now, we need to calculate the angular displacement when the tub is in motion. Substituting the values:

θ = 0.5 * (3.89 / 9.58) * (9.58)²

Simplifying gives us the angular displacement:

θ = 0.5 * (3.89) * (9.58)

Finally, we need to convert the angular displacement into revolutions by dividing by 2π (as there are 2π radians in one revolution):

Number of revolutions = θ / (2π)

Now, you can use the calculated angular displacement to find the number of revolutions the tub turns while it is in motion.