PHY motion 問題!!!

[匿名]

2009-11-14 5:20 am

A runner runs in a 100m race. The starter fires his gun at time t =0. The runner has a reaction time of 0.3s. Then at t=0.3, he accelerates from 0m/s to 8m/s until t=4. He runs with uniform velocity of 8m/s from t=4 to t=14.65s. It is given that his acceleration is 2.16m/s^2 and the average velocity during the race is6.83s. After some hard training, the runner improves his acceleration and maximum velocity by 5%respectively. Assuming that his reaction time doesn't change, how much better will he perform in 100m races?

回答 (1)

Prof. Physics

2009-11-14 5:46 pm

✔ 最佳答案

New acceleration, a = (1 + 5%)(2.16) = 2.268 ms^-2

New maximum velocity, v = (1 + 5%)(8) = 8.4 ms^-1

Consider the journey when he is accelerating,

by v = u + at

8.4 = 0 + (2.268)t

Time, t = 3.70 s

By v^2 = u^2 + 2as

(8.4)^2 = 0 + 2(2.268)s

Displacement, s = 15.56 m

So, the displacement left, s' = 100 - 15.56 = 84.44 m

And the time required to cover this displacement, t' = 84.44/8.4 = 10.05 s

So, the time required for the race = 0.3 + 3.70 + 10.05 = 14.06 s

He will perform (14.65 - 14.06) = 0.59 s better

參考: Physics king

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