dvhtlbz的部落格

標題:

Application of diff and int

發問:

http://holland.pk/1n3M

最佳解答:

(a) dS/dt = 7t+5 S = ∫ (7t+5) dt [ t from 0 to 4] S = 7t2 + 5t | [ t from 0 to 4] S = 7(4)2 + 5(4) = 132 m (b) Distance travel by car A from 0 to T = 7T2 + 5T | [ t from 0 to T] .... (1) Distance travel by car B from 5 to T S = ∫ (9t-42) dt [ t from 5 to T] S = 9t2 - 42t | [ t from 5 to T] S = 9T2 - 42T -[9(5)2 - 42(5)] S = 9T2 - 42T -15 When distance travel by car A = When distance travel by car B 7T2 + 5T = 9T2 - 42T -15 2T2 - 47T -15 = 0 T = 23.8 s or -0.315 s(reject) (c) S = 7t2 + 5t | [ t from 0 to 23.8] = 7(23.8)2 + 5(23.8) = 4084 m 2013-12-29 23:50:37 補充： 注意 : Vb = 9t - 42 when t = 23.8 Vb = 172.2 m/s = 620 km/h 時速 620 公里的車實在太快啦！所以，這條只是數學題，並不真實。 唔怪得 二十幾秒會行咗四公里咁多啦！

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