Question

A Shaft of an electric motor starts from rest and on the application of a torque, it gains an angular acceleration a=3t-t2, during the first 2 sacs. after which a=0 . The angular velocity after 2 seconds will be?

Answer 1

$$\begin{gathered} \alpha =3t-t^2 \\ angularvelocity=\theta =\alpha dt \\ \theta =\left(3t-t^2\right)dt \\ \theta =3t^2/2-t^3/3 \\ att=2s \\ \theta =\frac{3\times 4}{2}-\frac{8}{3}=10/3 \end{gathered}$$