The displacement (in feet) of a particle moving in a straight line is given by s= - 9t + 19, where t is measured in seconds. (a) Find the average velocity (in ft/s) over each time interval.
The displacement (in feet) of a particle moving in a straight line is given by s= - 9t + 19, where t is measured in seconds. (a) Find the average velocity (in ft/s) over each time interval.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
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![The displacement (in feet) of a particle moving in a straight line is given by s = t2 – 9t + 19, where t is measured in seconds.
2
(a) Find the average velocity (in ft/s) over each time interval.
(i) [4, 8]
ft/s
(ii) [6, 8]
ft/s
(iii) [8, 10]
ft/s
(iv) [8, 12]
ft/s
(b) Find the instantaneous velocity (in ft/s) when t = 8.
ft/s
(c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then select the graph of s with the tangent line whose slope is the instantaneous velocity in part (b).
S
S
S
15
15
20
20
10
10
10
10
5
t
13
10
15
10
15
10
15
10
-5
-5
- 10
- 10
- 10
- 10
- 20
-20
- 15
- 15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a03efe2-d931-4461-b3ce-5e694888ce83%2F8e62f2e4-8534-48c9-8df3-f832bd730095%2F5sbt595_processed.png&w=3840&q=75)
Transcribed Image Text:The displacement (in feet) of a particle moving in a straight line is given by s = t2 – 9t + 19, where t is measured in seconds.
2
(a) Find the average velocity (in ft/s) over each time interval.
(i) [4, 8]
ft/s
(ii) [6, 8]
ft/s
(iii) [8, 10]
ft/s
(iv) [8, 12]
ft/s
(b) Find the instantaneous velocity (in ft/s) when t = 8.
ft/s
(c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then select the graph of s with the tangent line whose slope is the instantaneous velocity in part (b).
S
S
S
15
15
20
20
10
10
10
10
5
t
13
10
15
10
15
10
15
10
-5
-5
- 10
- 10
- 10
- 10
- 20
-20
- 15
- 15
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