Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
11.3) question 9
![6. Explain why it is not possible to have an average velocity
with a large magnitude but a small average speed.
Problems
In Exercises 7-10, a position function 7(t) is given. Find v(t)
and a(t).
7. 7(t) = (2t+1, 5t — 2, 7)
8. 7(t) = (31²-2t+ 1, −ť² + t + 14)
9. 7(t)= (cost, sin t)
10. 7(t) = (t/10,- cost, sin t)
In Exercises 11-14, a position function 7(t) is given. Sketch
7(t) on the indicated interval. Find (t) and ä(t), then add
V(to) and a (to) to your sketch, with their initial points at 7(to),
for the given value of to.
11. F(t) = (t, sin t) on [0, π/2]; to = π/4
12. 7(t) = (t², sin t²) on [0, π/2]; to = √π/4
13. 7(t) = (t + t, -t² + 2t) on [-2, 2]; to = 1
14. 7(t) =
2t+3
t² + 1
on [-1, 1]; to = 0
In Exercises 15-24, a position function 7(t) of an object is
given. Find the speed of the object in terms of t, and find
where the speed is minimized/maximized on the indicated
interval.
15. 7(t) = (t², t) on [-1, 1]
16. 7(t) = (t,t-t³) on [-1,1]
on
In Exercis
objects an
intervals.
(a) Sh
to
(b) Fim
obi
25. 71 (t) =
72 (s) =
26. 7₁ (t) =
7₂ (s) =
27. 71(t) =
72 (s) =
28. 7₁ (t) =
72 (s) =
In Exercises
given its acce
29. a(t) = (2
30. ä(t) = (2,
31. ä(t) = (co
32. ā(t) = (0,
In Exercises 33
average velocit
on the given in
33. An object wit
where distan
onds, on [0, 2](https://content.bartleby.com/qna-images/question/400b9bd7-cb38-477d-bca9-0a4702f014e3/6c3a21b2-0afb-4edd-b079-ee9ea45c1b4b/lsre0bg_processed.jpeg)
Transcribed Image Text:6. Explain why it is not possible to have an average velocity
with a large magnitude but a small average speed.
Problems
In Exercises 7-10, a position function 7(t) is given. Find v(t)
and a(t).
7. 7(t) = (2t+1, 5t — 2, 7)
8. 7(t) = (31²-2t+ 1, −ť² + t + 14)
9. 7(t)= (cost, sin t)
10. 7(t) = (t/10,- cost, sin t)
In Exercises 11-14, a position function 7(t) is given. Sketch
7(t) on the indicated interval. Find (t) and ä(t), then add
V(to) and a (to) to your sketch, with their initial points at 7(to),
for the given value of to.
11. F(t) = (t, sin t) on [0, π/2]; to = π/4
12. 7(t) = (t², sin t²) on [0, π/2]; to = √π/4
13. 7(t) = (t + t, -t² + 2t) on [-2, 2]; to = 1
14. 7(t) =
2t+3
t² + 1
on [-1, 1]; to = 0
In Exercises 15-24, a position function 7(t) of an object is
given. Find the speed of the object in terms of t, and find
where the speed is minimized/maximized on the indicated
interval.
15. 7(t) = (t², t) on [-1, 1]
16. 7(t) = (t,t-t³) on [-1,1]
on
In Exercis
objects an
intervals.
(a) Sh
to
(b) Fim
obi
25. 71 (t) =
72 (s) =
26. 7₁ (t) =
7₂ (s) =
27. 71(t) =
72 (s) =
28. 7₁ (t) =
72 (s) =
In Exercises
given its acce
29. a(t) = (2
30. ä(t) = (2,
31. ä(t) = (co
32. ā(t) = (0,
In Exercises 33
average velocit
on the given in
33. An object wit
where distan
onds, on [0, 2
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