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The following data are recorded for the velocity of an object as a function of time (Table 2). t, s v, m/s 0 0 Table 2 4 12 16 8 20 24 28 32 36 34.7 61.8 82.8 99.2 112.0 121.9 129.7 135.7 140.4 a) Using 5-point central difference formula, estimate the object's acceleration at t = 28s. b) By assuming the exact acceleration at t = 28s is 1.625ms-2, find the error from the estimation in (a). (Your answer must be in 4 decimal points) c) Using 5-point central difference formula, estimate the second derivative of obiect's velocity at t = 24s.

The following data are recorded for the velocity of an object as a function of time (Table 2). t, s v, m/s 0 0 Table 2 4 12 16 8 20 24 28 32 36 34.7 61.8 82.8 99.2 112.0 121.9 129.7 135.7 140.4 a) Using 5-point central difference formula, estimate the object's acceleration at t = 28s. b) By assuming the exact acceleration at t = 28s is 1.625ms-2, find the error from the estimation in (a). (Your answer must be in 4 decimal points) c) Using 5-point central difference formula, estimate the second derivative of obiect's velocity at t = 24s.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 7E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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The following data are recorded for the velocity of an object as a function of time (Table 2). Table 2 t, s v, m/s 0 0 4 8 34.7 61.8 12 16 20 24 28 32 36 82.8 99.2 112.0 121.9 129.7 135.7 135.7 140.4 a) Using 5-point central difference formula, estimate the object's acceleration at t = 28s. b) By assuming the exact acceleration at t = 28s is 1.625ms-2, find the error from the estimation in (a). (Your answer must be in 4 decimal points) c) Using 5-point central difference formula, estimate the second derivative of obiect's velocity at t = 24s.
Transcribed Image Text:The following data are recorded for the velocity of an object as a function of time (Table 2). Table 2 t, s v, m/s 0 0 4 8 34.7 61.8 12 16 20 24 28 32 36 82.8 99.2 112.0 121.9 129.7 135.7 135.7 140.4 a) Using 5-point central difference formula, estimate the object's acceleration at t = 28s. b) By assuming the exact acceleration at t = 28s is 1.625ms-2, find the error from the estimation in (a). (Your answer must be in 4 decimal points) c) Using 5-point central difference formula, estimate the second derivative of obiect's velocity at t = 24s.
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