題目條件：

從傳送帶最大速度開始向下查找第一個滿足題目條件的值即可

import math from matplotlib import pyplot as plt import numpy as npdef T(t,v,T15,T6,T7,T89):#每段溫度a=[0,25,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,25]a=[i/v*60 for i in a]m=0a=[m:=m+i for i in a]Tair=25lmd0=-0.5c0=(T15-Tair)/(math.e**(-lmd0*25/v*60))lmd=0.015c=(T89-Tair)/(math.e**(-lmd*339.5/v*60))if t<a[1]:return c0*math.e**(-lmd0*t)+Tairelif t<a[10]:return T15elif t<a[11]:return T15+(T6-T15)/(a[11]-a[10])*(t-a[10])elif t<a[12]:return T6elif t<a[13]:return T6+(T7-T6)/(a[13]-a[12])*(t-a[12])elif t<a[14]:return T7elif t<a[15]:return T7+(T89-T7)/(a[15]-a[14])*(t-a[14])elif t<a[18]:return T89else:return c*math.e**(-lmd*t)+Tairdef k(t,v):#牛頓冷卻模型中每段的k值，k值計算可以看我第一問的求解a=[0,25,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,5,30.5,25]a=[i/v*60 for i in a]m=0a=[m:=m+i for i in a]if t<a[1]:return 0.0128elif t<a[11]:return 0.0177elif t<a[13]:return 0.0171elif t<a[15]:return 0.0242elif t<a[18]:return 0.0216else:return 0.0276def test(v):#測試是否滿足題目條件t_list=np.linspace(0,400,801).tolist()u_list=[25]for i in t_list:kk=k(i,v)*(T(i,v,182,203,237,254)-u_list[-1])if abs(kk)>3:return Falseu_list.append(u_list[-1]+kk*0.5)u_list.pop()if len([i for i in u_list if i>=150 and i<=190])<60/0.5 or len([i for i in u_list if i>=150 and i<=190])>120/0.5:return Falseif len([i for i in u_list if i>=217])<40/0.5 or len([i for i in u_list if i>=270])>90/0.5:return Falsemax=np.array(u_list).max()if max>250 or max<240:return Falsereturn Truedef main():for i in map(lambda x:x*0.01,range(78*100,73*100,-1)):if test(i):return iif __name__=='__main__':print(main())

得出最大速度78.0

def draw():v=78.0t_list=np.linspace(0,400,801).tolist()u_list=[25]for i in t_list:u_list.append(u_list[-1]+k(i,78.0)*(T(i,v,182,203,237,254)-u_list[-1])*0.5)u_list.pop()plt.plot(t_list,u_list)plt.show()

總結

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