A particle is projected with speed u against a constant acceleration of magnitude a and returns to its starting position after time T. Its average speed during the interval from t=0 to 3T/4 is:
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A particle is projected with speed u against a constant acceleration of magnitude a and returns to its starting position after time T. Its average speed during the interval from t=0 to 3T/4 is:

G1 Physics · Accepted Answer

The complete return time is T = 2u/a. Thus 3T/4 = 3u/(2a). The particle turns at t=u/a. Distance up to the turning point: s₁ = u²/(2a). During the next time u/(2a), starting from rest at the turning point, it travels back: s₂ = (a/2)[u/(2a)]² = u²/(8a). Total distance = 5u²/(8a). Total time = 3u/(2a). Average speed = [5u²/(8a)]/[3u/(2a)] = 5u/12.