Answer:
Approximately 0.343miles/hour
Step-by-step explanation:
Given the stopping distance of a car expressed as d = 0.05s² + 1.1s
If a car stops in 200 feet, the fastest it could have been traveling when the driver applied the brakes can be gotten by substituting S = 200ft into the equation above and solving the resulting quadratic equation.
Converting 200ft to miles
1 foot = 0.000189 mile
200feet = 200×0.000189
= 0.0378miles
The equation becomes:
0.0378 = 0.05s² + 1.1s
Multiplying through by 10000
378 = 500s²+11000s
500s²+11000s-378 = 0
Using the general formula
s = -b±√b²-4ac/2a
a = 500 b = 11000, c = -378
s = -11000±√11000²-4(500)(-378)/2(500)
s = -11000±√121,000.000+756000/1000
s = -11000±√121,756,000/1000
s = -11000±11,034.3/1000
s = -11000+11,034.3/1000
s = 34.3/1000
s = 0.0343miles/hour
Disregarding the negative value, the fastest it could have been traveling when the driver applied the brakes will be approximately 0.0343miles/hour.
