a. Explanation Given: The velocity of the function Car A v A ( t ) = 88 t t + 1 . The velocity of the function Car B v B ( t ) = 88 t 2 ( t + 1 ) 2 . The velocity of the function Car C v C ( t ) = 88 t 2 t 2 + 1 . Calculation: Consider s A ( t ) is the displacement of car A . Compute the displacement of car A as follows, s A ( t ) = ∫ v A ( t ) d t = ∫ 88 t t + 1 d t = 88 ∫ ( 1 − 1 t + 1 ) d t = 88 ( t − ln | t + 1 | ) + C That is, s A ( t ) = 88 ( t − ln | t + 1 | ) + C (1) Substitute 0 for t in the above equation and use s A ( 0 ) = 0 . s A ( 0 ) = 88 ( 0 + ln | 0 + 1 | ) + C C = 0 Substitute C = 0 in equation (1), s A ( t ) = 88 ( t − ln | t + 1 | ) + 0 = 88 ( t − ln | t + 1 | ) That is, s A ( t ) = 88 ( t − ln | t + 1 | ) (2) Consider s B ( t ) is the displacement of car B . Compute the displacement of car B as follows, s B ( t ) = ∫ v B ( t ) d t = ∫ 88 t 2 ( t + 1 ) 2 d t = 88 ∫ t 2 ( t + 1 ) 2 d t = 88 ∫ t 2 t 2 + 2 t + 1 d t That is, s B ( t ) = 88 ∫ t 2 t 2 + 2 t + 1 d t (3) Simplify the term of the integrand by using long division method. t 2 + 2 t + 1 1 t 2 t 2 + 2 t + 1 − 2 t − 1 ¯ That is, t 2 t 2 + 2 t + 1 = 1 + − 2 t − 1 t 2 + 2 t + 1 . Substitute t 2 t 2 + 2 t + 1 = 1 + − 2 t − 1 t 2 + 2 t + 1 in equation (3), s B ( t ) = 88 ∫ ( 1 + − 2 t − 1 t 2 + 2 t + 1 ) d t = 88 ∫ ( 1 − 2 t + 2 t 2 + 2 t + 1 + 1 ( t + 1 ) 2 ) d t = 88 [ t − ln | t 2 + 2 t + 1 | − 1 t + 1 ] + C That is, s B ( t ) = 88 [ t − ln | t 2 + 2 t + 1 | − 1 t + 1 ] + C (4) Substitute 0 for t in the above equation and use s B ( 0 ) = 0 b. To determine To find: The car which is travels farthest on time the interval 0 ≤ t ≤ 5 . c. To determine To find: The position function for each car. d. To determine To find: The car which is ultimately gains the lead.

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

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ISBN: 9780134996103

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 8.5, Problem 93E

To determine

To find: The car which is travels farthest on time the interval 0≤t≤1.

To determine

To find: The car which is travels farthest on time the interval 0≤t≤5.

To determine

To find: The position function for each car.

To determine

To find: The car which is ultimately gains the lead.

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Chapter 8.5, Problem 92E

Chapter 8.5, Problem 94E

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Chapter 8 Solutions

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 8.1 - What change of variable would you use for the...Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - What change of variables would you use for the...Ch. 8.1 - Prob. 2E Ch. 8.1 - What trigonometric identity is useful in...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E

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The car which is travels farthest on time the interval 0 ≤ t ≤ 1 .

Solution Summary: The author calculates the displacement of car A as follows: s_A(t)=88t+1

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To find: The car which is travels farthest on time the interval 0≤t≤1.

To find: The car which is travels farthest on time the interval 0≤t≤5.

To find: The position function for each car.

To find: The car which is ultimately gains the lead.

Want to see the full answer?

Chapter 8 Solutions