In class, we used a numerical method to determine the velocity of an object at t = 2.00 s given that the object had started from rest at t= 0s and accelerated at a rate given by a(t) = (8.00 m/s) ť². Here's what we did: 1. Divided t into four intervals of 0.5 s each. 2. For each interval, calculated the average a. These were the numerical values we obtained for each time interval: i t (s) a, (m/s²) After summing the values according to: 1 0.25 0.50 2 0.75 4.50 3 1.25 12.50 V₂ -v₁ = lima At 4 we arrived at the approximate value v = 21.0 m/s. 4 1.75 24.50 a (m/s²) 32.00+ 24.00+ 16.00 8.00+ ā az az a4 0 0 0.50 1.00 1.50 2.00 -t (s) We then proceeded to integrate to obtain the analytical solution, which was v = 21.33 m/s. Using the same numerical method, divide t into eight and then sixteen intervals to calculate the approximate value for v at t = 2.00 s. This should demonstrate that with more sampling, the AUC (area under the curve) value converges toward the analytical solution. Make two tables similar to the one above, showing the t and a values for each interval, and then sum the areas.

In class, we used a numerical method to determine the velocity of an object at t = 2.00 s given that the object had started from rest at t= 0s and accelerated at a rate given by a(t) = (8.00 m/s) ť². Here's what we did: 1. Divided t into four intervals of 0.5 s each. 2. For each interval, calculated the average a. These were the numerical values we obtained for each time interval: i t (s) a, (m/s²) After summing the values according to: 1 0.25 0.50 2 0.75 4.50 3 1.25 12.50 V₂ -v₁ = lima At 4 we arrived at the approximate value v = 21.0 m/s. 4 1.75 24.50 a (m/s²) 32.00+ 24.00+ 16.00 8.00+ ā az az a4 0 0 0.50 1.00 1.50 2.00 -t (s) We then proceeded to integrate to obtain the analytical solution, which was v = 21.33 m/s. Using the same numerical method, divide t into eight and then sixteen intervals to calculate the approximate value for v at t = 2.00 s. This should demonstrate that with more sampling, the AUC (area under the curve) value converges toward the analytical solution. Make two tables similar to the one above, showing the t and a values for each interval, and then sum the areas.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 18PQ: Acceleration a has the dimensions of length per time squared, speed v has the dimensions of length...

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