20.51 The distance required to stop an automobile consists of both thinking and

Question

20.51 The distance required to stop an automobile consists of both thinking and braking components each of which is a function of its speed. The following experimental data was collected to quantify this relationship. Develop a best-fit equation for both the thinking and braking components. Use these equations to estimate the total stopping distance for a car traveling at 110 km/hr. Speed, km/hr 30 45 60 75 90 120 Thinking, m 5.6 8.5 11.1 14.5 16.7 22.4 Braking, m 5.0 12.3 21.0 32.9 47.6 84.7 (Answer found to be 91.8754m please verify)

Explanation / Answer

Now we apply single variate linear regression taking thinking distance as dependant and speed as independent. We obtain the following equation:

Thinking Distance (m) = 0.1854*(speed) + 0.1784

Then we apply single variate linear regression taking braking distance as dependant and speed as independent. We obtain the following equation:

Braking distance (m) = 0.9748*(speed) - 36.3324

Thus, Total stopping distance(m) = 1.1632*(speed) - 36.1540

At speed 110 km/h, total stopping distance = 1.1632*110 - 36.154 = 91.798 m which is nearly equal to the value you mentioned.

Note: I have performed the regression analysis using MS Excel. Kindly let me know if you need help on that. Here is a link that you may use http://www.wikihow.com/Run-a-Multiple-Regression-in-Exce
l

Speed(km/h) Thinking(m) Braking(m) 30 5.6 5 45 8.5 12.3 60 11.1 21 75 14.5 32.9 90 16.7 47.6 120 22.4 84.7

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.