Suppose a certain object moves in a straight line with the following velocity, where v is in meter per second and t is in seconds. v (t) = - 2 + t = 3sin (pit). Without using your calculator, but instead, using properties of definite integrals and facts you know about area. determine the net change in distance of the object from time t=0 to time t=6 seconds. And find the object's average velocity in this interval.

Question

Mathematics

Waylon

16 June, 10:39

Suppose a certain object moves in a straight line with the following velocity, where v is in meter per second and t is in seconds. v (t) = - 2 + t = 3sin (pit). Without using your calculator, but instead, using properties of definite integrals and facts you know about area. determine the net change in distance of the object from time t=0 to time t=6 seconds. And find the object's average velocity in this interval.

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Amelie Harrell · Answer 1

The given function is

v (t) = - 2 + t - sin (πt)

The next change in the distance from 0 to 6 is

v (0) = 0

v (6) = 4

(4 - 0) / (6 - 0) = 2/3

The average velocity in the interval is

∫v (t) dt from 0 to 6

= - 2t + t²/2 + 6πcos πt from 0 to 6

= - 2 (6) + 36/2 - 6 - (0 + 0 + 1)

= - 1