Physics

Physics

Problem

The angular position of a wheel is given by θ=4t2−t3\theta = 4t^{2} - t^{3}, where θ\theta is in radians and tt in seconds. Which pair gives (instantaneous angular velocity at t=2 st = 2\,\text{s}, average angular velocity between t=0t = 0 and t=2 st = 2\,\text{s})? a) (12 rad s−1,  4 rad s−1)(12\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1}) b) (4 rad s−1,  4 rad s−1)(4\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1}) c) (4 rad s−1,  8 rad s−1)(4\,\text{rad s}^{-1},\;8\,\text{rad s}^{-1}) d) (−4 rad s−1,  4 rad s−1)(-4\,\text{rad s}^{-1},\;4\,\text{rad s}^{-1})

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