Recall that if s(t) represents the position at time t of any object moving in a straight line, then its velocity is given by the derivative  v(t) = s'(t). Now, suppose that object is a car. Since a car rarely drives at a constant speed, the velocity itself may be changing. The rate at which the velocity is changing is the acceleration. Because the derivative measures the rate of change, acceleration is the derivative of velocity  a(t) = v'(t). So, to determine acceleration, first find velocity. Given that  s(t) = 130 + 13t − 0.8t2,  the velocity  v(t)  is found by taking the  ---Select--- first second third derivative of position,  s'(t). Since  s'(t) = 13 −       t,  we have  v(t) =

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
icon
Concept explainers
Question
Recall that if s(t) represents the position at time t of any object moving in a straight line, then its velocity is given by the derivative 
v(t) = s'(t).
Now, suppose that object is a car. Since a car rarely drives at a constant speed, the velocity itself may be changing. The rate at which the velocity is changing is the acceleration. Because the derivative measures the rate of change, acceleration is the derivative of velocity 
a(t) = v'(t).
So, to determine acceleration, first find velocity.
Given that 
s(t) = 130 + 13t − 0.8t2,
 the velocity 
v(t)
 is found by taking the  ---Select--- first second third derivative of position, 
s'(t).
Since 
s'(t) = 13 − 
 
  
 
t,
 we have 
v(t) = 
 
 
 
 .
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Application of Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning