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3. What is the average velocity of the particle from Exercise 2, over the fol-
lowing intervals?
(a) t = 0 . . . 1?
(b) t = 1 . . . 2?
(c) t = 0 . . . 2?
(d) t = 5.5 . . . 6.5?
(e) t = 0 . . . 9?
4. Write a similar piece-wise function v(t) that describes the velocity of the
the particle from Exercise 2 at time t. In this case, the velocity is not
defined at the “junctions” between the pieces, so only worry about what
happens in the middle of each piece. (This is unfortunately one of those
finer points we had to skip over.)
5. What is the instantaneous velocity of the particle from Exercise 2 at the
following times?
(a) t = 0.1
(b) t = 1.0
(c) t = 1.9
(d) t = 4.1
(e) t = 5
(f) t = 6.5
(g) t = 8
(h) t = 9
6. Write a similar piece-wise function a(t) that describes the acceleration of
the particle from Exercise 2 at time t. Once again, don't worry about what
happens at the junction points.
7. What is the particle's acceleration at the following times?
(a) t = 0.1
(b) t = 1.0
(c) t = 1.9
(d) t = 4.1
(e) t = 5
(f) t = 6.5
(g) t = 8
(h) t = 9
8. What physical situation is signified by a negative discriminant in Equa-
tion (11.16), resulting in complex solutions? What if the discriminant is
zero and there is only one solution?
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