Question 1190843: 5. When the driver of a vehicle observes an obstacle in the road, the total stopping distance involves both the reaction distance (the distance the vehicle travels, while the driver moves his or her foot to the brake pedal) and the breaking distance (the distance the vehicle travels once the brakes are applied) For a car traveling at a speed of v miles per hour the reaction distance R, in feet, can be estimated by R(v)=2.2v. Suppose that braking distance B, in feet, for a car is given by B(v)=0.05v^2+0.4v-15.
a) Find the stopping distance function: D(v)
b) What is the domain of D(v)?
c) Find the stopping distance if the car is traveling at a speed of 60mph.
d) Change the stopping distance to miles and explain what your answer to part c) this problem means?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Part (a)
Add the reaction distance and braking distance functions to get the overall stopping distance
D(v) = R(v) + B(v)
D(v) = 2.2v + 0.05v^2 + 0.4v - 15
D(v) = 0.05v^2 + 2.6v - 15
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Part (b)
In general, the domain is the set of all allowed inputs of the function.
More specifically, the domain is the set of real numbers on the interval  where M is the max speed of the car.
This max speed is not stated in the instructions, so we cannot describe the domain's endpoints purely in a numeric sense. You may have to contact your teacher for clarification.
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Part (c)
Plug v = 60 into the result found in part (a)
D(v) = 0.05v^2 + 2.6v - 15
D(60) = 0.05(60)^2 + 2.6(60) - 15
D(60) = 321
The stopping distance is 321 feet.
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Part (d)
The D(v) function found in part (a) is the stopping distance in feet.
To convert from feet to miles, we divide by 5280.
D(v) = stopping distance in feet
E(v) = stopping distance in miles
E(v) = ( D(v) )/5280
E(v) = (0.05v^2 + 2.6v - 15)/5280
Then if we wanted to plug in v = 60 for instance, then,
E(v) = (0.05v^2 + 2.6v - 15)/5280
E(60) = (0.05(60)^2 + 2.6(60) - 15)/5280
E(60) = 321/5280
E(60) = 0.06079545454546
The stopping distance of 321 feet is roughly equivalent to 0.0608 miles.
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