Concept explainers
That at some time during the race, the acceleration of both the cars are same.
Explanation of Solution
Given information:
In an automobile race along a straight road, car A passes car B twice.
Calculations:
Let
Let
Now it is given that A passes B twice, therefore there exist (at least) three times when their positions are equal.
Let,
Now position of the cars at time
By the mean value theorem, there exists a time
Applying the mean value theorem again, this time to the function
Now,
so
Thus we can see that the acceleration of both the cars are same at some time
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning