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#1 2007-04-17 13:55:42
- virtualinsanity
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- Registered: 2007-03-11
- Posts: 38
Calculus problem
I found this calc problem in a chapter on improper integration. If anyone could explain how it is done, I would greatly appreciate it!
A car is travelling at 55 mph. The driver sees a traffic jam ahead and hits the brakes. Brakes apply friction. The car's velocity satisfies the differential equation v' = -1080v miles per hour per hour. How far does the car go after the brake is applied?
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#2 2007-04-17 15:49:55
- George,Y
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- Registered: 2006-03-12
- Posts: 1,379
Re: Calculus problem
V'/V=-1080
(ln|v|)'=-1080
v>0
(lnv)'=-1080
lnv=-1080t+C
v=A e[sup]-1080t[/sup]
t=0, v=A=55
v=55e[sup]-1080t[/sup]
Integrate v from 0 to +infinity you may get the answer.
The answer is 55/1080
X'(y-Xβ)=0
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#3 2007-04-19 02:30:54
- George,Y
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- Registered: 2006-03-12
- Posts: 1,379
Re: Calculus problem
Note you that:
(ln|f(x)|)'= f'(x)/f(x) when x≠0
X'(y-Xβ)=0
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