The angular position of a wheel is given by

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

\theta = 4t^{2} - t^{3}

, where

\theta

is in radians and

t

in seconds. Which pair gives (instantaneous angular velocity at

t = 2\,\text{s}

, average angular velocity between

t = 0

and

t = 2\,\text{s}

)? (a)

(12\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1})

(b)

(4\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1})

(c)

(4\,\text{rad s}^{-1},\;8\,\text{rad s}^{-1})

(d)

(-4\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1})