A particle moves for equal time intervals with velocities +v, +2v and -v. The ratio average speed / magnitude of average velocity is:
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A particle moves for equal time intervals with velocities +v, +2v and −v. The ratio average speed / magnitude of average velocity is:

G1 Physics · Accepted Answer

Let each interval be τ. Distance = (v+2v+v)τ = 4vτ. Displacement = (v+2v−v)τ = 2vτ. Total time = 3τ. Hence average speed / |average velocity| = distance/|displacement| = 4vτ/(2vτ) = 2.