A rotating toy above a baby's crib makes one complete counterclockwise rotation in 1 min.
a. What is its angular displacement in 3 min?
b. What is the toy's angular velocity in rad/min?
c. If the toy is turned off, does it have positive or
negative angular acceleration? Explain.

(a) The angular displacement of the toy is 18.85 rad.

(b) The toy's angular velocity is 6.284 rad/min.

(c) if the counterclockwise rotation is in negative direction, the angular acceleration will be positive when the toy is turned off and vice versa.

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the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.