The answer is A. 50 m/s
I took the test and completed the study guide in class and got it correct.
Let's break the problem into two parts:
1) In the first part, the wheel starts with an angular speed
and it rotates with an angular acceleration of
for t=1.80 s. So we can find the total angle covered by the wheel in this part of the motion:
2) Now, the circuit breaker trips, so the wheel starts to decelerate with a certain angular acceleration
(which is negative). During this part of the motion, the wheel covered an angle of
.
3) So, we just need to add the angles the wheel covered in the two parts of the motion:
D = 0.9 km = 900 m, distance moved
v = 35 nm/s , the speed
v = 35 x 10⁻⁹ m/s
= (35 x 10⁻⁹ m/s)*(365 days/y)*(24*60*60 s/day)
= 1.1038 m/y
The time iaken is
t = d/v
= (900 m)/(1.1038 m/y)
= 815.365 y
Answer: 815.4 y (nearest tenth)