A particle is projected along +x with speed u and then moves with constant acceleration -a. Consider its motion from t=0 to t=3u/a. The ratio of average speed to magnitude of average velocity is:
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A particle is projected along +x with speed u and then moves with constant acceleration −a. Consider its motion from t=0 to t=3u/a. The ratio of average speed to magnitude of average velocity is:

G1 Physics · Accepted Answer

The particle stops at t=u/a. Distance to the turning point: s₁ = u²/(2a). At t=3u/a, x = u(3u/a) − (a/2)(9u²/a²) = −3u²/(2a). From the turning point at +u²/(2a) to the final point −3u²/(2a), distance is s₂ = 2u²/a. Total distance: s = 5u²/(2a). Magnitude of displacement: |Δx| = 3u²/(2a). Therefore the ratio is [5u²/(2a)]/[3u²/(2a)] = 5/3.