物理功課>.難題 急急急急急

醉酒司機初速度 = 20 m/s
清醒司機初速度 = 15 m/s

(a) 醉酒司機在停下前的制動距離:
v2 - u2 = 2as
- 400 = 2(-8)s
s = 25 m

清醒司機在停下前的制動距離:
v2 - u2 = 2as
- 225 = 2(-9)s
s = 12.5 m

兩者的總制動距離 = 37.5 m, 所以兩車會相撞

(b) 假設相撞發生於他們踏下制動器後的 t 秒發生, 則:

醉酒司機制動距離 = ut + at2/2
= 20t - 4t2

清醒司機制動距離 = ut + at2/2
= 15t - 4.5t2

兩車相撞時, 總制動距離為 30 m, 所以:

35t - 8.5t2 = 30
17t2 - 70t + 60 = 0

t = 1.22 s 或 2.90 s

惟完全停下前, 清醒司機制動時間為 15/9 = 1.6 s
在 (a) 部已證明兩車完全停下前已相撞, 所以 t = 1.22 s

而醉酒司機制動距離 = 20 x 1.22 - 4 x 1.222 = 18.4 m

(c) 醉酒司機速度 v = u + at = 20 - 1.22 x 8 = 10.3 m/s
清醒司機速度 v = u + at = 15 - 1.22 x 9 = 4.1 m/s

a.清醒司機開車的初速度=-54*1000/3600=-15m/s
醉酒司機開車的初速度=72*1000/3600=20m/s
設S1為清醒司機踏下制動器後行駛的距離
v^2-u^2=2aS1
0-(-15)^2=2(9)-S1
S1=12.5m
設S2為醉酒司機踏下制動器後行駛的距離
v^2-u^2=2aS2
0-(20)^2=2(-8)S2
S2=25m

兩車行數的總距離=S1+S2=25+12.5
=32.5m
因為兩車所行的距離>30m
所以兩車會相撞

b.設t為兩車相撞的時間
S=ut+0.5at^2
=20t+0.5(-8)t^2---(1)
相似地
-S'=-15t+0.5(9)t^2
S'=15t-0.5(9)t^2
因為兩撞在同一時間
S+S'=30m
所以20t-4t^2+15t-4.5t^2=30m
35t-8.5t^2=30
t=1.22s/2.9s(排徐)---(3)

代(3)-->(1)
20(1.22)-4(1.22)^2=18.45m
所以撞車地點距離醉酒司機踏下制動器的起點為18.45m

C.設v1和v2分別為醉"""的最後速度和清醒""""的最後速度
v1=u+at
v1=20+(-8)(1.22)
v1=10.24m/s

v2=u+at
v2=-15+(9)(1.22)
v2=-4.02m/s

所以醉""""的最後速度為10.24m/s
清醒""""的最後速度為-4.02m/s

2009-10-24 03:31:16 補充：
上面果位阿生你錯得好搞笑下~但點解會係博士- -仲要擅長物理- -

Since you have already done part (a), I only give you the solution for (b) and (c).

(b) Let d (in metres) be the distance covered by the drunk driver, the distance covered by the other driver = (30-d) m

Using equations of motion: s = ut + (1/2).a.t^2
For the drunk driver,
u = 72/3.6 m/s = 20 m/s, a = -8 m/s2, s = d, t =?
hence, d = 20t + (1/2)(-8)t^2 --------------- (1)

For the other driver:
u = - 54/3.6 m/s =-15 m/s a = 9 m/s2, s = 30-d, t=?
hence, 30-d = -15t + (1/2)(9)t^2 --------------- (2)

adding (1) and (2):
30 = 5t + (1/2)t^2
i.e. 60 = 10t + t^2
or t^2 + 10t - 60 = 0
solve for t gives t = 4.22 s or t = -14.2 s (rejected)
Hence, distance covered by drunk driver before collision
= 20 x 4.22 + (1/2)(-8)(4.22)^2 m

(c) Using equation of motion: v = u + a.t
For the drunk driver,
u = 20 m/s, a = -8 m/s2, t = 4.22 s, v = ?
hence, v = (20 - 8 x 4.22) m/s

For the other driver,
u = -15 m/s a = 9 m/s2, t = 4.22 s, v = ?
hence, v =[ -15+(9 x 4.22)] m/s