Program Explanation Given information: The graph of the velocity function of a particle that travels along the straight line is redrawn as shown in Figure 1. Graph: It is observed from Figure 1 that the particle starts from the origin and in the interval of time [ 0 , 5 ] the velocity function is in linear form. Therefore, the velocity function is t The relation between velocity function and the position function can be expressed as, v ( t ) = d x d t Therefore, the position function can be expressed as, x ( t ) = ∫ v ( t ) d t = ∫ t d t = t 2 2 + C The particle starts at the origin. Therefore, the initial position x ( 0 ) = 0 . Now apply the condition ofthe initial position x 0 = 0 to obtain the value of C . 0 = 5 t + C C = 0 Substitute 0 for C in the equation x ( t ) = t 2 2 + C to obtain the particular solution. x ( t ) = t 2 2 + 0 x ( t ) = t 2 2 Therefore, the position function is x ( t ) = t 2 2 in the interval of time [ 0 , 5 ] . The velocity function is v ( t ) = 5 in the interval of time [ 5 , 10 ] . Therefore, the position function can be expressed as, x ( t ) = ∫ v ( t ) d t = ∫ 5 d t = 5 t + C Therefore, the general position function for the interval is x ( t ) = 5 t + C . Since, the position function is x ( t ) = t 2 2 . Substitute 5 for t in equation x ( t ) = t 2 2 to obtain the corresponding value of x ( 5 ) . x ( 5 ) = 25 2 Therefore, the value of x ( 5 ) is 12

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

Question

Chapter 1.2, Problem 20P

Program Plan Intro

To sketch: The graph of the position function x(t) for 0≤t≤10 .

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Chapter 1.2, Problem 19P

Chapter 1.2, Problem 21P

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Chapter 1 Solutions

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The graph of the position function x ( t ) for 0 ≤ t ≤ 10 .

Solution Summary: The author illustrates the graph of the velocity function of a particle that travels along the straight line as shown in Figure 1.

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To sketch: The graph of the position function x(t) for 0≤t≤10 .

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Chapter 1 Solutions