Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.

Question
Asked Jan 13, 2020
14 views

Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.

check_circle

Expert Answer

Step 1

Find ds/dv using first derivative and exponent rule of derivative.

Calculus homework question answer, step 1, image 1
fullscreen
Step 2

To find ds/dv at v = 35 , plug v=35 in ds/dv.

Answer: 4.88 ft / mph

Interpretation: Rate ...

Calculus homework question answer, step 2, image 1
fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other