Thomas Calculus 13th [Solutions]

Section 3.4 The Derivative as a Rate of Change 143
(c) body changes direction at t 6.25 sec
(d) body speeds up on (6.25, 12.5] and slows down on [0, 6.25)
(e) The body is moving fastest at the endpoints t 0 and t 12.5 when it is traveling 200 ft/sec. Its moving
slowest at t 6.25 when the speed is 0.
(f ) When t 6.25 the body is s 625 m from the origin and farthest away.
34.
(a) v 0 when t 3
2 sec
(b) v 0 when 0 t 1.5 body moves left (down); v 0 when 1.5 t 5 body moves right (up)
(c) body changes direction at t 3
2 sec
(d) body speeds up on 3 2 , 5 and slows down on 0,
3
2
(e) body is moving fastest at t 5 when the speed | v (5)| 7 units/sec; it is moving slowest at t
3
when
2
the speed is 0
(f ) When t 5 the body is s 12 units from the origin and farthest away.
35.
(a) v 0
(b) v 0 when
(c)
6 15
sec
3
6 15 6 15
3 3
when t
6 15
t body moves left (down); v 0 when 0 t or 6 15
3 3
body moves right (up)
6 15
body changes direction at t sec
(d) body speeds up on
3
6 15 6 15
3 3
, 2 , 4 and slows down on
6 15 6 15
0, 2, .
3 3
(e) The body is moving fastest at t 0 and t 4 when it is moving 7 units/sec and slowest at
6 15
3
(f ) When t the body is at position s 6.303 units and farthest from the origin.
t
t
4
6 15
sec
3
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