Question

a remote controlled car's wheel accelerates at 22.4 rad/s^2. if the wheel begins with an angular speed of 10.8 rad/s what is the wheel's angular speed after exactly 3 full turns?

Answer 1

3 full turns is 6 pi radians.
Call the angular speed at the end of 3 turns w(3).
The three turns require time T, where
w(3) = 10.8 + 22.4*T
[w(3)+ 10.8]*T/2 = 6 pi

T = 12 pi/[w(3)+ 10.8]
= [w(3)-10.8]/22.4
w(3)^2 - (10.8)^2 = 22.4*(12 pi)
Solve for w(3)