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# approximation of the acceleration and anti-derivative v(t)dt

The graph of the velocity v(t), in ft/sec, of a car traveling on a straight road, for 0 is greater than or equal to t is greater than or equal to 50, is shown in the attachment. A table of values for v(t), at 5 second intervals of time t, is also in the attachment.

a.) During what intervals of time is the acceleration of the car positive? Give a reason for your answer.

b.) Find the average acceleration of the car, in ft/sec^2, over the interval 0 is greater than or equal to t is greater than or equal to 50

c.) Find one approximation for the acceleration of the car, in ft/sec^2, at t=40. Show the computations you used to arrive at your answer.

d.) Approximate anti-derivative v(t)dt of intervals 50 and 0 with Riemann sum, using the right endpoint of five subintervals of equal length. Using correct units, explain the meaning of this integral.

#### Solution Summary

It shows how to find the approximation of the acceleration and anti-derivative v(t)dt with Riemann sum. The solution is detailed and received a '5/5' rating from the student who originally posted the questions.

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