A particle has velocity +10 m s⁻¹ at t=0 and -20 m s⁻¹ at t=6 s under constant acceleration. The ratio average speed / magnitude of average velocity during this interval is:
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A particle has velocity +10 m s⁻¹ at t=0 and −20 m s⁻¹ at t=6 s under constant acceleration. The ratio average speed / magnitude of average velocity during this interval is:

G1 Physics · Accepted Answer

Constant acceleration: a = (−20−10)/6 = −5 m s⁻². The particle stops at 10−5t=0 ⇒ t=2 s. Distance from 0 to 2 s: average speed = (10+0)/2 = 5, so distance = 10 m. Distance from 2 to 6 s: speed rises from 0 to 20 in 4 s, so distance = (0+20)(4)/2 = 40 m. Total distance = 50 m, average speed = 50/6 = 25/3 m s⁻¹. Displacement = [(10−20)/2](6) = −30 m. Magnitude of average velocity = 30/6 = 5 m s⁻¹. Required ratio = (25/3)/5 = 5/3.