EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 23, Problem 12P
The following data are provided for the velocity of an object as a function of time,
| t, s | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
| v, m/s | 0 | 34.7 | 61.8 | 82.8 | 99.2 | 112.0 | 121.9 | 129.7 | 135.7 | 140.4 |
(a) Using the best numerical method available, how far does the object travel from
(b) Using the best numerical method available, what is the object's acceleration at
(c) Using the best numerical method available, what is the object's acceleration at
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A SpaceX rocket has just launched, and the below table shows it's altitude versus time. Using only this data, calculate the best estimation of the rocker's acceleration at time=4.5 seconds.
time (s) altitude (m)
0.0
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3.0
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ⒸA. 36.9 m/s²
ⒸB. 57.0 m/s2
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E. 102.2 m/s²
(b) A rocket is launched from the ground. Its acceleration a measured every 5 seconds is tabulated below.
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(iii) Can you apply Simpson's 3/8 rule in this case?
15
48.5 51.25 54.35 59.48
t
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64.3
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An automotive engineer is testing how quickly a newly designed sports car accelerates from rest. He has collected data giving the velocity V, in miles per hour, as a function of time t, in seconds, since the car was at rest. Below is a table giving a portion of his data.
Time (t)
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2.0
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2.5
33.9
3.0
39.4
3.5
44.9
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Time
2.0 to 2.5
2.5 to 3.0
3.0 to 3.5
Change in t
Change in V
(b) What is the slope for the linear function modeling velocity as a function of time? mph per secExplain in practical terms the meaning of the slope.
This means that, after every second, the car will be going miles per hour faster. This says that the acceleration is ---Select--- varying constant .
(c) Use the data in the table to find the formula for velocity V as a linear function of time t that is valid over the time period covered in the table.V =…
Chapter 23 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9PCh. 23 - Develop a user-friendly program to apply a Romberg...
Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...
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