9. Craig is traveling east-west along a straight path. Craig's velocity can be modeled by v(t) = -5t + t√t - 3 meters per minute for 0 ≤ t ≤ 30 minutes. (a) What is Craig's displacement over the interval 0 ≤ t ≤ 30 minutes? 200 ... DODE M (b) At what time (s) t, 0≤ t ≤ 30, is Craig's instantaneous acceleration equal to his average acceleration over the interval 0 ≤ t ≤ 30 minutes? (c) If Craig's starting location is 54 meters east of his home at time t = 0 and he is moving west, what is Craig's location relative to his home at time t = 22?
9. Craig is traveling east-west along a straight path. Craig's velocity can be modeled by v(t) = -5t + t√t - 3 meters per minute for 0 ≤ t ≤ 30 minutes. (a) What is Craig's displacement over the interval 0 ≤ t ≤ 30 minutes? 200 ... DODE M (b) At what time (s) t, 0≤ t ≤ 30, is Craig's instantaneous acceleration equal to his average acceleration over the interval 0 ≤ t ≤ 30 minutes? (c) If Craig's starting location is 54 meters east of his home at time t = 0 and he is moving west, what is Craig's location relative to his home at time t = 22?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9. Craig is traveling east-west along a straight path. Craig's velocity can be modeled by
v(t) = −5t+t√t - 3 meters per minute for 0 ≤ t ≤ 30 minutes.
(a) What is Craig's displacement over the interval 0 ≤ t ≤ 30 minutes?
(d) At time t = 5, is Craig's speed increasing or decreasing? Justify.
(b) At what time(s) t, 0≤ t ≤ 30, is Craig's instantaneous acceleration equal to his average acceleration over the
interval 0 ≤ t ≤ 30 minutes?
(e) What is Craig's total distance traveled during the time interval 0 ≤ t ≤ 30 ?
(c) If Craig's starting location is 54 meters east of his home at time t = 0 and he is moving west, what is Craig's
location relative to his home at time t = 22?
t minutes
m(t) meters
m' (t) meters/min
2
(f) Jocelyn is walking along the same path. Selected values of her velocity and positions on the path relative to Craig's
home are given in the table. Find m' (t) dt and interpret the value in the context of this problem with units.
10
0
3
25
2
55
45
00
5
90
-35
nons
DOD
10
20
-25
PO
12
0
0
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Transcribed Image Text:9. Craig is traveling east-west along a straight path. Craig's velocity can be modeled by
v(t) = −5t+t√t - 3 meters per minute for 0 ≤ t ≤ 30 minutes.
(a) What is Craig's displacement over the interval 0 ≤ t ≤ 30 minutes?
(d) At time t = 5, is Craig's speed increasing or decreasing? Justify.
(b) At what time(s) t, 0≤ t ≤ 30, is Craig's instantaneous acceleration equal to his average acceleration over the
interval 0 ≤ t ≤ 30 minutes?
(e) What is Craig's total distance traveled during the time interval 0 ≤ t ≤ 30 ?
(c) If Craig's starting location is 54 meters east of his home at time t = 0 and he is moving west, what is Craig's
location relative to his home at time t = 22?
t minutes
m(t) meters
m' (t) meters/min
2
(f) Jocelyn is walking along the same path. Selected values of her velocity and positions on the path relative to Craig's
home are given in the table. Find m' (t) dt and interpret the value in the context of this problem with units.
10
0
3
25
2
55
45
00
5
90
-35
nons
DOD
10
20
-25
PO
12
0
0
Solution
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