Answer to Question #127188 in Physics for Ukachukwu blessing

Question

A body on the circular orbit makes an angular displacement given by(t)= 2t²+5t+5r, if t is in seconds calculate the angular velocity at t= 2s

Answer 1

By definition, the angular velocity is:

$$\omega(t) = \dfrac{d\phi(t)}{dt}$$

where $\phi(t) = 2t^2 + 5t + 5$ is the angular displacement. Thus, have:

$$\omega(t) = \dfrac{d\phi(t)}{dt} = 4t+5 \space (rad/s)$$

At t= 2s:

$$\omega(2s) = 4\cdot 2s + 5 = 8+5=13\space rad/s$$

Answer. 13 rad/s.