Concept explainers
(a)
To prove: The distance traveled by the object between times
(a)
Explanation of Solution
Proof:
The formula for distance is,
Speed varies over times so speed v is a function time t, the speed at time
Thus, the area under the curve of a speed function between time a to b determines the distance traveled by object between times
(b)
To find: The distance traveled by the car from
(b)
Answer to Problem 4P
The distance travelled by the car is 66.67 ft.
Explanation of Solution
Given:
The speed of the car is,
Calculation:
Calculate the area under the curve
The formula of area is,
Formula to calculate the value of
Substitute 0 for a and 5 for b in equation (2) to find the value of
Substitute 0 for a and
Find the value of
Substitute
The value of,
Substitute
Substitute
The distance traveled by the car is equal to the area A.
Thus, the distance travelled by the car is 66.67 ft.
Chapter 13 Solutions
Precalculus: Mathematics for Calculus - 6th 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