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Three start-ups Three cars, A, B, and C, start from rest

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 79E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 79E

Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions:

a. After t = 1 s, which car has traveled farthest?

b. After t = 5 s, which car has traveled farthest?

c. Find the position functions for the three cars assuming that all cars start at the origin

d. Which car ultimately gains the lead and remains in front?

Step-by-Step Solution:

Problem 79E

Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions:

a. After t = 1 s, which car has traveled farthest?


b. After t = 5 s, which car has traveled farthest?


c. Find the position functions for the three cars assuming that all cars start at the origin


d. Which car ultimately gains the lead and remains in front?

Answer;

   Step 1 of  3 ;

          Given velocity functions are : , and .

  1. In this problem we need to  find  after  t =1s,  which car has  traveled farthest.

          At  t = 1 seconds :  =  = 44

                                         =  = = 22

                                    =   = = 44

              Therefore , after t = 1s car A and car C  has traveled  farthest.

Step 2 of  3;

b) In this problem we need to  find  after  t =5s,  which car has  traveled farthest.

          At  t = 5 seconds :  =  = 73.333

                                         =  = = 61.1111

                                    =   = = 84.615

              Therefore , after t = 5s car C  has traveled  farthest.

Step 3 of 3 ;

               In this problem we need to find the  position functions  for  the three cars assuming  that  all cars  start at the origin.

Let us find the position function of  A :

                           (t)=  = 88dt

   By using partial fractions  we get :   = -

             Hence ,  (t) = 88dt = 88-)dt

                                                   = 88 (dt)

                                                   = 88( t - ln (1+t)) +C , since dx = ln |x| +c

   We know that , at initial point t = 0 .

  So ,  (0) = 0 = 88(  0 - ln (1+0)) +C

           

              0 = C , since ln(1) = 0

     Therefore , the position function of  A is :   (t) =  88(  t - ln (1+t)).

  Let us find the position function of  B :

                           (t) =  = 88dt

   By using partial fractions  we get :   =  + -

             Hence ,  (t) = 88dt  = 88+- )dt

                                                   = 88 (dt - dt)

                                                   = 88( t -  - 2 ln (1+t)) +C , since dx = ln |x| +c and  = n

   We know that , at initial point t = 0 .

  So , (0) = 0 = 88( 0 -  - 2 ln (1+0)) +C

              0 =  -88 +C  , since ln(1) = 0

            C = 88

     Therefore , the position function of  B is :   (t) =  88( t -  - 2 ln (1+t)) + 88

  Let us find the position function of  C :

                           (t) =  = 88dt

   By using partial fractions  we get :   =

             Hence ,  (t) = 88dt  = 88 -)dt

                                                   = 88 (dt)

                                                   = 88( t - ) +C , since dx = +c .   We know that , at initial point t = 0 .

  So , (0) = 0 = 88( 0 - ) +C

              0 =  0 +C  , since  = 0

            C = 0

     Therefore , the position function of  C is :   (t) =  88( t - )

 

d)  From  step-2  , it is clear that  car C  ultimately gains the lead and remains in front.  

     

Step 2 of 3

Chapter 7.4, Problem 79E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This full solution covers the following key subjects: Car, start, cars, traveled, farthest. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 79E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Three start-ups Three cars, A, B, and C, start from rest and accelerate along a line according to the following velocity functions: a. After t = 1 s, which car has traveled farthest?________________b. After t = 5 s, which car has traveled farthest?________________c. Find the position functions for the three cars assuming that all cars start at the origin________________d. Which car ultimately gains the lead and remains in front?” is broken down into a number of easy to follow steps, and 69 words. Since the solution to 79E from 7.4 chapter was answered, more than 283 students have viewed the full step-by-step answer.

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