Find the angle through which the part rotates before reaching this final speed.

A machine part rotates at an angular speed
of 0.85 rad/s; its speed is then increased to
3.16 rad/s using an angular acceleration of
0.76 rad/s

Find the angle through which the part rotates before reaching this final speed.
Answer in units of rad

u = 0.85 rad/s; its speed is then increased to
v =3.16 rad/s angular acceleration a=0.76 rad/s2

v^2 =u^2 +2as
3.16^2 = 0.85^2 + 2* 0.76 * s
s = 6.09 rad
answer

We have
w1 = 0.85 rad/s
w2 = 3.16 rad/s
α = 0.76 rad /s^2

Using

w2^2 = w1^2 + 2αѲ

Ѳ = (w2^2 - w1^2) / 2α = (3.16^2 - 0.85^2) / (2 * 0.76) = 6.1 rads