
Modeling Data
The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour)is the distance R (in meters) the car travels during the reaction time of the driver plus die distance B (in meters)the car travels after the brakes are applied (see figure).The table shows the results of an experiment.
Speed, v | 20 | 40 | 60 | 80 | 100 |
Reaction Time Distance, R | 8.3 | 16.7 | 25.0 | 33.3 | 41.7 |
Braking Time Distance, B | 2.3 | 9.0 | 20.2 | 35.8 | 55.9 |
(a) Use the regression capabilities of a graphing utility to find a linear model for reaction time distance R.
(b) Use the regression capabilities of a graphing utility to find a quadratic model for braking time distance B.
(c) Determine the polynomial giving the total stopping distance T.
(d) Use a graphing utility to graph the functions R, B, and T in the same viewing window.
(e) Find the derivative of T and the rates of change of the total stopping distance for v = 40, v = 80, and v = 100.
(f) Use the results of this exercise to draw conclusions about the total stopping distance as speed increases.

Trending nowThis is a popular solution!

Chapter 2 Solutions
Calculus
- Explain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.arrow_forwarduse Cauchy Mean-Value Theorem to derive Corollary 12.6.2, and then derive 12.6.3arrow_forward
- Explain the focus and reasons for establishment of 12.5.1(lim(n->infinite) and sigma of k=0 to n)arrow_forwardExplain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges.arrow_forwardExplain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forward
- Use identity (1+x+x2+...+xn)*(1-x)=1-xn+1 to derive the result of 12.2.2. Please notice that identity doesn't work when x=1.arrow_forwardExplain the key points and reasons for the establishment of 11.3.2(integral Test)arrow_forwardTo explain how to view "Infinite Series" from "Infinite Sequence"’s perspective, refer to 12.2.1arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning





