A person walks into a room and switches on the ceiling fan. The fan accelerates

Question

A person walks into a room and switches on the ceiling fan. The fan accelerates with constant angular acceleration for 18 until it reaches its operating angular speed of 1.6 - after that its speed remains constant as long as the switch is "on". The person stays in the room for a short time; then, 5.5 minutes after turning the fan on, she switches it off again and leaves the room. The fan now decelerates with constant angular acceleration, taking 2.4 minutes to come to rest.

What is the total number of revolutions made by the fan, from the time it was turned on until the time it stopped?

Explanation / Answer

since the unit are not given in the problem i assumed that the all the unit are consist of revolution and second. like acceleration are in revolution/s2 and velocity are in revolution/s.

 =  0 + *t

1.6 = 0 + 18*t

t = 0.0888 s.

 2 = 02+2**s

1.62 = 02 + 2*18*S

s = 0.0711

now the speed will be constant 1.6 

so the distance travelled in (5.5*60-0.0888)sec  will be

s = 1.6*(5.5*60-0.0888) = 527.8579

now the fan started decelerating

 =  0 - *t

0 = 1.6 - *(2.4*60)

= 0.0111

2 = 02 - 2**s

02 = 1.62 - 2*(0.0111*s)

s = 115.315

so total rotation will be = 115.315 + 527.8579 + 0.0711 = 643.244 revolution.

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