The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 3.0 rev/s in 13.0 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 12.0 s. Through how many revolutions does the tub turn during this 25 s interval

The tub turns 37.520 revolutions during the 25-second interval.

Explanation:

The total number of revolutions done by the tub of the washer (), in revolutions, is the sum of the number of revolutions done in the acceleration (), in revolutions, and deceleration stages (), in revolutions:

(1)

Then, we expand the previous expression by kinematic equations for uniform accelerated motion:

(1b)

Where:

- Angular accelerations for acceleration and deceleration stages, in revolutions per square second.

- Acceleration and deceleration times, in seconds.

And each acceleration is determined by the following formulas:

Acceleration

(2)

Deceleration

(3)

Where is the maximum angular velocity of the tub of the washer, in revolutions per second.

If we know that , and , then the quantity of revolutions done by the tub is:

The tub turns 37.520 revolutions during the 25-second interval.

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