Re: [問題] 一題運動學的題目請高手解一下
※ 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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※ 編輯: hcldesmond 來自: 222.166.244.211 (03/28 08:13)
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