A particle is projected vertically upward with speed u. Find its average speed during the interval 0≤t≤3u/g.
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A particle is projected vertically upward with speed u. Find its average speed during the interval 0≤t≤3u/g.

G1 Physics · Accepted Answer

The particle reaches the highest point at t=u/g. Maximum height: H = u²/(2g). At t=3u/g, y = u(3u/g) − (g/2)(9u²/g²) = −3u²/(2g). Distance from the highest point to the final point: H − y = u²/(2g) + 3u²/(2g) = 2u²/g. Total distance: H + 2u²/g = 5u²/(2g). Total time = 3u/g. Average speed = [5u²/(2g)]/[3u/g] = 5u/6.