國中教甄｜理化理化102 年第 24 題單選題

A wheel rotates with angular acceleration given by α = $4 t^{3}$ – $3 t^{2}$ . If the angular velocity is 30 radians per second at t = 0, find the angle turned through by the wheel between times t = 3 and t = 5 seconds. Answer in radians.

A260

B320

C380

D500正確答案

答案與詳解

正確答案

α 隨時間變化，要用積分：ω = t⁴ − t³ + 30，再從 t = 3 積到 t = 5：Δθ = (5⁵ − 3⁵)/5 − (5⁴ − 3⁴)/4 + 30 × 2 = 576.4 − 136 + 60 = 500.4 ≈ 500 rad。

A260✕ 錯誤

與積分結果 500.4 rad 不符。

B320✕ 錯誤

與積分結果 500.4 rad 不符。

C380✕ 錯誤

D500✓ 正確

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精選詳解

A wheel rotates with angular acceleration given by α = 4t3 – 3t2. If the angular velocity is 30 radians per second at t = 0, find the angle turned through by the wheel between times t = 3 and t = 5 seconds. Answer in radians.