The angular velocity of a process control motor is (21−(1/2t^2)) rad/s, where t is in seconds.
1.) At what time does the motor reverse direction?
2.) Through what angle does the motor turn between t =0 s and the instant at which it reverses direction?
angular velocity of a process control motor is (21−(1/2t^2)) rad/s
The Attempt at a Solution
For part 1 I just set the equation equal to 0 and got a time of 6.5 sec, which is correct
For part 2, I have no idea what to do. Nothing is working, so if you could help, that would be great! I have tried taking the derivative to find acceleration, which is -t, and then plugging that into θf = θi + ωi(t) + 1/2a(t^2). I set θi = 0 because I figured there would initially be no angle. I set ωi = 21 because at t=0, ω = 21. I set t= 6.5, and a=-6.5...so my equation was θf = 0 + 21(6.5s) + 1/2(-6.5)(6.5s^2), but the answer came to like -0.8125 rad? is that right? it seems odd to me...