Explanation Given data: The toy car moves back and forth on a long, straight track for 4 minutes such that the function S ( t ) = 96 t − 84 t 2 + 28 t 3 − 3 t 4 describe how far the car is to the right of starting point in cm, after t minutes. Method/Formula used: The farthest point means S ( t ) is maximum. Calculation: The function that describe the distance of toy car from the starting point is S ( t ) = 96 t − 84 t 2 + 28 t 3 − 3 t 4 ............ (1) Differentiating result (1), with respect to‘ t’ d S d t = 96 − 168 t + 84 t 2 − 12 t 3 Thus, the velocity of the toy car at time‘ t’ is given by v = 96 − 168 t + 84 t 2 − 12 t 3

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.4, Problem 49A

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To find: The time, the toy car is moving fastest to the right and fastest to the left.

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Chapter 3.4, Problem 48A

Chapter 3.4, Problem 50A

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The time, the toy car is moving fastest to the right and fastest to the left.

Solution Summary: The author analyzes how the toy car moves on a long, straight track for 4 minutes. The graph of velocity ( v in cm/min) is shown in figure.

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