Answer
a) $\omega_0=117.2rad/s$
b) $t=141s$
Work Step by Step
We have: final speed $\omega=137rad/s$, acceleration $\alpha=0.14rad/s^2$ and angular displacement $\theta=2870rev\times\Big(\frac{2\pi rad}{1rev}\Big)=1.8\times10^4rad$
a) The turbine's initial velocity is $$\omega^2=\omega_0^2+2\alpha\theta$$ $$\omega_0^2=\omega^2-2\alpha\theta=13729$$ $$\omega_0=117.2rad/s$$
b) The amount of time elapsed is $$t=\frac{\omega-\omega_0}{\alpha}=141s$$
