A particle executes one-dimensional motion according to x = A cosωt. For 0 ≤ t ≤ 3π/(2ω), the ratio average speed / magnitude of average velocity is:
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A particle executes one-dimensional motion according to x = A cosωt. For 0 ≤ t ≤ 3π/(2ω), the ratio average speed / magnitude of average velocity is:

G1 Physics · Accepted Answer

At t=0, x=A. At t=π/ω, x=−A. At t=3π/(2ω), x=0. Total distance = A to −A: 2A plus −A to 0: A = 3A. Magnitude of displacement = |0−A| = A. Therefore average speed / |average velocity| = 3A/A = 3.