Through how many revolutions does the tub turn while its is in motion?

A tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 8.00 s, at which time it is turning at 5.00 rev/s. At this point, the person doing the laundry opens the lid and a safety switch turns off the machine. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn while its is in motion?Through how many revolutions does the tub turn while its is in motion?Consider linear motion with acceleration v = u + at and v^2 = u^2 + 2as



Here angular angle described p (or turns of revolution) is comparable to s, acceleration alpha (written a) is comparable to a, v and u are comparable to angular speed omega (written w). So then,



while speeding up: a = w/t = 5/8 revs/s^2

p = w^2 / 2a = 5^2 / 2 (5/8) = ... revs



while stopping: a = -w/t = -5/12 revs/s^2

p = -w^2 / 2a = 5^2 / 2 (5/12) = ... revs



Adding the two, the total turns = ... revs











20+30 = 50 revs

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