※ 引述《enterNTU (發發)》之銘言： : Car B is traveling a distance d ahead of car A. : Both cars are traveling at 20 m/s when the driver of B suddenly : applies the brakes,causing his car to decelerate at 4 m/s^2 . : it takes the driver of A 0.75 second to react. when driver of A : applies his brakes,he decelerates at 5 m/s^2. determine the distance d : between the cars so as to avoid a collision. : car A |...............| car B ..............|| : d ---------------以下是錯誤解答-------------- For car A, Reaction distance r = reaction time * speed A 2 2 By v = v + 2a(x-x ) , 0 0 2 2 v - v 0 Braking distance b = ──── A 2a 　　　　　　　　　　　　　 A Stopping distance s = r + b A A A For car B, 2 2 By v = v + 2a(x - x ), 0 0 2 2 　　　　　　　　　　　　v - v 0　　 Stopping distance s = ──── B 2a B d = s - s A B --------------以上是錯誤解答--------------- 抱歉，剛剛才發現car A最後會比car B慢 所以以上的方法是錯的 首先要找出何時car A的速度等於car B 設此時t = t ，car B煞車時t = 0 f By v = v + at, 0 car A: v = v + a (t - 0.75) (1) 0 A f car B: v = v + a t (2) 0 B f (1) = (2): v + a (t - 0.75) = v + a t 0 A f 0 B f 0.75a A t = ─── f a - a A B 1 2 By x - x = v t + -at , 0 0 2 At t = t , f 1 2 distance traveled by car A d = (v * 0.75) + [v (t -0.75) + -a (t -0.75) ] A 0 0 f 2 A f 1 2 distance traveled by car B d = v t + -a t B 0 f 2 B f d = d - d = 5.6m A B --

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