t 0. 36 9 12 (seconds) p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P, where time t is measured in seconds and p(t) is measured in feet. Selected values of p (t) are shown in the table above. (a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to 12 approximate the value of | p(t)dt Show the computations that lead to your answer.
t 0. 36 9 12 (seconds) p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P, where time t is measured in seconds and p(t) is measured in feet. Selected values of p (t) are shown in the table above. (a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to 12 approximate the value of | p(t)dt Show the computations that lead to your answer.
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...
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### Particle Motion Problem
Consider the table of values for a particle, \( A \), moving along the x-axis. The movement is modeled by a twice-differentiable function \( p \), where time \( t \) is in seconds and position \( p(t) \) is in feet. The selected values are provided below:
| \( t \) (seconds) | 0 | 3 | 6 | 9 | 12 |
|-------------------|---|---|---|---|----|
| \( p(t) \) (feet) | 3 | 5.5 | 7 | 13 | 17 |
**(a)** Use a midpoint Riemann sum with two subintervals of equal length and the given table values to approximate the value of \(\int_{0}^{12} p(t) \, dt\). Show your computations.
**(b)** Using the data in the table, approximate \( p'(10) \) by calculating the average rate of change of \( p(t) \) over the interval \( 9 \leq t \leq 12 \). Show your calculations, including the units.
**(c)** Interpret the meaning of \( p'(10) \) within the context of this problem.
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