Question

The angular displacement of a gear is Ttar=(2t^2-9t+4)radians.calculate it's angular velocity and angular accelerations at t=25

Answer 1

The angular velocity is the first derivative of displacement by time:

$$v(t)=x'(t)=2·2t^{2-1}-1·9t^{1-1}=4t-9,\\ v(25)=4·25-9=91\text{ rad/s}.$$

The angular acceleration is the second derivative of displacement by time, or the first derivative of velocity by time:

$$a(t)=v'(t)=4\text{ rad/s}^2.$$